Hp 17Bii Users Manual Plus E PRINT 030709

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File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

HP 17bII+ Financial Calculator

Owner’s Manual

Edition 1

Part Number F2234-90020

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

Notice

For warranty and regulatory information for this calculator, see the owner’s

manual.

This manual and any examples contained herein are provided “as is” and

are subject to change without notice. Hewlett-Packard Company makes no

warranty of any kind with regard to this manual, including, but not

limited to, the implied warranties of merchantability and fitness for a

particular purpose. Hewlett-Packard Co. shall not be liable for any errors or

for incidental or consequential damages in connection with the furnishing,

performance, or use of this manual or the examples contained herein.

Reproduction, adaptation, or translation of this manual is prohibited without

prior written permission of Hewlett-Packard Company, except as allowed

under the copyright laws.

The programs that control your calculator are copyrighted and all rights are

reserved. Reproduction, adaptation, or translation of those programs without

prior written permission of Hewlett-Packard Co. is also prohibited.

4995, Murphy Canyon Rd,

Suite 301

San Diego,CA 92123

Printing History

Edition 1 June 2003

Welcome to the hp17bII+ 3

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Welcome to the HP 17bII+

The HP 17bII+ is part of Hewlett-Packard’s new generation of calculators:

! The two-line display has space for messages, prompts, and labels.

! Menus and messages show you options and guide you through problems.

! Built-in applications solve these business and financial tasks:

! Time Value of Money. For loans, savings, leasing, and amortization.

! Interest Conversions. Between nominal and effective rates.

! Cash Flows. Discounted cash flows for calculating net present value

and internal rate of return.

! Bonds. Price or yield on any date. Annual or semi-annual coupons;

30/360 or actual/actual calendar.

! Depreciation. Using methods of straight line, declining balance,

sum-of-the-years’ digits, and accelerated cost recovery system.

! Business Percentages. Percent change, percent total, markup.

! Currency Exchange. Exchange calculations between two currencies.

! Statistics. Mean, correlation coefficient, linear estimates, and other

statistical calculations.

! Clock. Time, date, and appointments.

! Use the Solver for problems that aren’t built in: type an equation and then

solve for any unknown value. It’s easier than programming!

! There are 28K bytes of memory to store data, lists, and equations.

! You can print information using the HP 82240 Infrared Printer.

! You can choose either ALG (Algebraic) or RPN (Reverse Polish Notation)

entry logic for your calculations.

4 Contents

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Contents

13 List of Examples

16 Important Information

1 17 Getting Started

17 Power On and Off; Continuous Memory

17 Adjusting the Display Contrast

18 Setting the Language

18 What You See in the Display

19 The Shift Key (@)

19 Backspacing and Clearing

21 Doing Arithmetic

22 Keying in Negative Numbers (&)

22 Using the Menu Keys

23 The MAIN Menu

25 Choosing Menus and Reading Menu Maps

27 Calculations Using Menus

28 Exiting Menus (e)

28 Clearing Values in Menus

29 Solving Your Own Equations (SOLVE)

30 Typing Words and Characters: the ALPHAbetic

31 Editing ALPHAbetic Text

32 Calculating the Answer (CALC)

34 Controlling the Display Format

34 Decimal Places

34 Internal Precision

34 Temporarily SHOWing ALL

35 Rounding a Number

35 Exchanging Periods and Commas in Numbers

Contents 5

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36 Error Messages

36 Modes

37 Calculator Memory (@M)

2 38 Arithmetic

38 The Calculator Line

38 Doing Calculations

40 Using Parentheses in Calculations

40 The Percent Key

40 The Mathematical Functions

41 The Power Function (Exponentiation)

42 The MATH Menu

43 Saving and Reusing Numbers

43 The History Stack of Numbers

44 Reusing the Last Result (@L)

45 Storing and Recalling Numbers

46 Doing Arithmetic Inside Registers and Variables

47 Scientific Notation

48 Range of Numbers

3 49 Percentage Calculations in Business

50 Using the BUS Menus

50 Examples Using the BUS Menus

50 Percent Change (%CHG)

51 Percent of Total (%TOTL)

52 Markup as a Percent of Cost (MU%C)

52 Markup as a Percent of Price (MU%P)

53 Sharing Variables Between Menus

4 54 Currency Exchange Calculation

54 The CURRX Menu

55 Selecting a Set of Currencies

57 Entering a Rate

6 Contents

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59 Converting between Two Currencies

59 Storing and Recalling Sets of Currencies

60 Clearing the Currency Variables

5 61 Time Value of Money

61 The TVM Menu

64 Cash Flow Diagrams and Signs of Numbers

66 Using the TVM Menu

67 Loan Calculations

71 Savings Calculations

74 Leasing Calculations

77 Amortization (AMRT)

78 Displaying an Amortization Schedule

81 Printing an Amortization Table

6 84 Interest Rate Conversions

85 The ICNV Menu

85 Converting Interest Rates

87 Compounding Periods Different from Payment Periods

7 91 Cash Flow Calculations

91 The CFLO Menu

92 Cash Flow Diagrams and Signs of Numbers

94 Creating a Cash-Flow List

95 Entering Cash Flows

97 Viewing and Correcting the List

98 Copying a Number from a List to the Calculator

Line

98 Naming and Renaming a Cash-Flow List

99 Starting or GETting Another List

99 Clearing a Cash-Flow List and Its Name

100 Cash-Flow Calculations: IRR, NPV, NUS, NFV

107 Doing Other Calculations with CFLO Data

Contents 7

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8 108 Bonds

108 The BOND Menu

110 Doing Bond Calculations

9 114 Depreciation

114 The DEPRC Menu

116 Doing Depreciation Calculations

116 DB, SOYD, and SL Methods

118 The ACRS Method

119 Partial-Year Depreciation

10 121 Running Total and Statistics

122 The SUM Menu

123 Creating a SUM List

123 Entering Numbers and Viewing the TOTAL

124 Viewing and Correcting the List

126 Copying a Number from a List to the Calculator

Line

126 Naming and Renaming a SUM List

127 Starting or GETting Another List

127 Clearing a SUM List and Its Name

127 Doing Statistical Calculations (CALC)

128 Calculations with One Variable

130 Calculations with Two Variables (FRCST)

133 Curve Fitting and Forecasting

138 Weighted Mean and Grouped Standard Deviation

139 Summation Statistics

140 Doing Other Calculations with SUM Data

11 141 Time, Appointments, and Date Arithmetic

141 Viewing the Time and Date

8 Contents

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142 The Time Menu

143 Setting the Time and Date (SET)

144 Changing the Time and Date Formats (SET)

144 Adjusting the Clock Setting (ADJST)

145 Appointments (APPT)

145 Viewing or Setting an Appointment (APT1-APT10)

147 Acknowledging an Appointment

148 Unacknowledged Appointments

148 Clearing Appointments

149 Date Arithmetic (CALC)

150 Determining the Day of the Week for Any Date

150 Calculating the Number of Days between Dates

151 Calculating Past or Future Dates

12 153 The Equation Solver

153 Solver Example : Sales Forecasts

156 The SOLVE Menu

157 Entering Equations

158 Calculating Using Solver Menus (CALC)

161 Editing an Equation (EDIT)

161 Naming an Equation

162 Finding an Equation in the Solver List

162 Shared Variables

162 Clearing Variables

163 Deleting Variables and Equations

164 Deleting One Equation or Its Variables (DELET)

164 Deleting All Equations or All Variables in the Solver

(@c)

164 Writing Equations

166 What Can Appear in an Equation

168 Solver Functions

174 Conditional Expressions with IF

176 The Summation Function (∑)

177 Accessing CFLO and SUM Lists from the Solver

178 Creating Menus for Multiple Equations

(S Function)

Contents 9

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179 How the Solver Works

180 Halting and Restarting the Numerical Search

181 Entering Guesses

13 184 Printing

185 The Printer’s Power Source

185 Double-Space Printing

185 Printing the Display(P)

186 Printing Other Information (@p)

186 Printing Variables, Lists, and Appointments (LIST)

188 Printing Descriptive Messages (MSG)

188 Trace Printing (TRACE)

189 How to Interrupt the Printer

14 190 Additional Examples

190 Loans

190 Simple Annual Interest

191 Yield of a Discounted (or Premium) Mortgage

193 Annual Percentage Rate for a Loan with Fees

195 Loan with an Odd (Partial) First Period

197 Canadian Mortgages

199 Advance Payments (Leasing)

200 Savings

200 Value of a Fund with Regular Withdrawals

202 Deposits Needed for a Child’s College Account

206 Value of a Tax-Free Account

208 Value of a Taxable Retirement Account

209 Modified Internal Rate of Return

213 Price of an Insurance Policy

215 Bonds

216 Discounted Notes

217 Statistics

217 Moving Average

219 Chi-Squared (χ2) Statistics

10 Contents

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A 222 Assistance, Batteries, Memory, and Service

222 Obtaining Help in Operating the Calculator

222 Answers to Common Questions

224 Power and Batteries

224 Low-Power Indications

225 Installing Batteries

227 Managing Calculator Memory

228 Resetting the Calculator

230 Erasing Continuous Memory

231 Clock Accuracy

231 Environmental Limits

231 Determining If the Calculator Requires Service

232 Confirming Calculator Operation: Self-Test

233 Warranty

235 Service

236 Regulatory information

237 Noise Declaration

B 238 More About Calculations

238 IRR% Calculations

238 Possible Outcomes of Calculating IRR%

239 Halting and Restarting the IRR% Calculation

239 Storing a Guess for IRR%

240 Solver Calculations

240 Direct Solutions

242 Iterative Solutions

246 Equations Used by Built-in Menus

246 Actuarial Functions

247 Percentage Calculations in Business (BUS)

247 Time Value of Money (TVM)

247 Amortization

248 Interest Rate Conversions

Contents 11

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248 Cash-Flow Calculations

215 Bond Calculations

250 Depreciation Calculations

251 Sum and Statistics

251 Forecasting

252 Equations Used in (Chapter 14)

252 Canadian Mortgages

253 Odd-Period Calculations

253 Advance Payments

253 Modified Internal Rate of Return

C 254 Menu Maps

D 261 RPN: Summary

261 About RPN

261 About RPN on the HP 17bII+

262 Setting RPN Mode

263 Where the RPN Functions Are

264 Doing Calculations in RPN

264 Arithmetic Topics Affected by RPN Mode

264 Simple Arithmetic

266 Calculations with STO and RCL

266 Chain Calculations－No Parentheses!

E 268 RPN: The Stack

268 What the Stack Is

269 Reviewing the Stack (Roll Down)

269 Exchanging the X- and Y-Registers in the Stack

270 Arithmetic－How the Stack Does It

271 How ENTER Works

272 Clearing Numbers

273 The LAST X Register

273 Retrieving Numbers from LAST X

12 Contents

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273 Reusing Numbers

274 Chain Calculations

275 Exercises

F 276 RPN: Selected Examples

283 Error Messages

289 Index

List of Examples 13

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List of Examples

The following list groups the examples by category.

Getting Started

25 Using Menus

29 Using the Solver

Arithmetic

40 Calculating Simple Interest

178 Unit Conversions

190 Simple Interest at an Annual Rate

(RPN example on page 276)

General Business Calculations

50 Percent Change

51 Percent of Total

52 Markup as a Percent of Cost

52 Markup as a Percent of Price

53 Using Shared Variables

159 Return on Equity

Currency Exchange Calculations

57 Calculating an Exchange Rate

58 Storing an Exchange Rate

59 Converting between Hong Kong and U.S Dollars

Time Value of Money

67 A Car Loan

68 A Home Mortgage

69 A Mortgage with a Balloon Payment

71 A Savings Account

14 List of Examples

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72 An Individual Retirement Account

74 Calculating a Lease Payment

75 Present Value of a Lease with Advanced Payments

and Option to Buy

80 Displaying an Amortization Schedule for a Home

Mortgage

82 Printing an Amortization Schedule

172 Calculations for a Loan with an Odd First Period

191 Discounted Mortgage

193 APR for a Loan with Fees

(RPN example on page 276)

194 Loan from the Lender’s Point of View

(RPN example on page 277)

196 Loan with an Odd First Period

197 Loan with an Odd First Period Plus Balloon

198 Canadian Mortgage

200 Leasing with Advance Payments

200 A Fund with Regular Withdrawals

202 Savings for College (RPN example on page 278)

207 Tax-Free Account (RPN example on page 280)

208 Taxable Retirement Account

(RPN example on page 282)

214 Insurance Policy

Interest Rate Conversions

86 Converting from a Nominal to an Effective Interest

Rate

89 Balance of a Savings Account

Cash Flow Calculations

97 Entering Cash Flows

102 Calculating IRR and NPV of an Investment

104 An Investment with Grouped Cash Flows

105 An Investment with Quarterly Returns

210 Modified IRR

List of Examples 15

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Bonds and Notes

111 Price and Yield of a Bond

112 A Bond with a Call Feature

113 A Zero-Coupon Bond

215 Yield to Maturity and Yield to Call

217 Price and Yield of a Discounted Note

Depreciation

117 Declining-Balance Depreciation

118 ACRS Deductions

120 Partial-Year Depreciation

Running Total and Statistical Calculations

125 Updating a Checkbook

128 Mean, Median, and Standard Deviation

134 Curve Fitting

138 Weighted Mean

218 A Moving Average in Manufacturing

220 Expected Throws of a Die ( 2

)

Time, Alarms, and Date Arithmetic

144 Setting the Date and Time

148 Clearing and Setting an Appointment

151 Calculating the Number of Days between Two Dates

152 Determining a Future Date

How to Use the Equation Solver

159 Return on Equity

166 Sales Forecasts

172 Using a Solver Function (USPV)

175 Nested IF Functions

181 Using Guesses to Find a Solution Iteratively

Printing

189 Trace-Printing an Arithmetic Calculation

16 Important Information

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Important Information

! Take the time to read chapter 1. It gives you an overview of how the

calculator works, and introduces terms and concepts that are used

throughout the manual. After reading chapter 1, you’ll be ready to

start using all of the calculator’s features.

! You can choose either ALG (Algebraic) or RPN (Reverse Polish

Notation) mode for your calculations. Throughout the manual, the

“v “in the margin indicates that the examples or keystrokes must be

performed differently in RPN. Appendixes D, E, and F explain how to

use your calculator in RPN mode.

! Match the problem you need to solve with the calculator’s capabilities

and read the related topic. You can locate information about the

calculator’s features using the table of contents, the subject index, the

list of examples, and the menu maps in appendix C (the gold-edged

pages).

! Before doing any time-value-of-money or cash-flow problems, refer to

pages 64 and 92 to learn how the calculator uses positive and

negative numbers in financial calculations.

! For a deeper treatment of specific types of calculations, refer to

chapter 14, “Additional Examples.” If you especially like learning by

example, this is a good reference spot for you.

1: Getting Started 17

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Getting Started

Watch for this symbol in the margin. It identifies examples

or keystrokes that are shown in ALG mode and must be

performed differently in RPN mode. Appendixes D, E, and F

explain how to use your calculator in RPN mode.

The mode affects only arithmetic calculations ― all other operations,

including the Solver, work the same in RPN and ALG modes.

Power On and Off; Continuous Memory

To turn on the calculator, press C (clear) (note ON printed below

the key). To turn it off, press @ and then C. This shifted function is

called o (note OFF printed above the key). Since the calculator has

Continuous Memory, turning it off does not affect the information you’ve

stored there.

To conserve energy, the calculator turns itself off after 10 minutes of no

use.

If you see the low battery symbol ( ) at the top of the display, you

should replace the batteries as soon as possible. Follow the instructions

on page 224.

Adjusting the Display Contrast

The display’s brightness depends on lighting, your viewing angle, and

the display contrast setting. To change the display contrast, hold down

the C key and press + or -.

18 1: Getting Started

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Setting the Language

The calculator can display information in six different languages. The

language initially used by the calculator was preset at the factory. To

change the language:

1. Press the @ >.

2. Press ! to display the INTL menu, which stands for

"international".

3. Press the appropriate menu key to change the language.

Table 1-1. Keys for language

Key Description

" #German

$ #English

% #Spanish

& #French

' !Italian

( #Portuguese

What You See in the Display

Menu Labels. The bottom line of the display shows the menu labels for

each of the six major menus (work areas) in the calculator. More about

these later in this chapter.

The Calculator Line. The calculator line is where you see numbers (or

letters) that you enter, and the results of calculations.

Annunciators. The symbols shown here are called annunciators.

Each one has a special significance.

1: Getting Started 19

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The Shift Key (@)

Some keys have a second, shifted function printed in color above the

key. The colored shift key accesses these operations. For example,

pressing and releasing @ , then pressing C turns the calculator off.

This is written @o.

Pressing @ turns on the shift annunciator ( ). This symbol stays on

until you press the next key. If you ever press @ by mistake, just press @

again to turn off the .

Backspacing and Clearing

The following keys erase typing mistakes, entire numbers, or even lists or

sets of data.

Shift (@ ) is

active.

(page 19)

Sending information

to the printer.

(page 184)

Alarm going off

(or past due).

(page 147)

Batteries low.

(page 224)

Calculator

line Cursor

Menu labels for the MAIN menu.

To display the MAIN menu, press

@A (that is, first @ , then

e).

Annunciators

20 1: Getting Started

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Table 1-2. Keys for Clearing

Key Description

< Backspace; erases the character before the cursor.

C Clear; clears the calculator line. (When the calculator

is off, this key turns the calculator on, but without

clearing anything.)

@c This clears all information in the current work area

(menu). For example, it will erase all the numbers in

a list if you are currently viewing a list (SUM or

CFLO). In other menus (like TVM), @c clears

all of the values that have been stored. In SOLVE, it

can delete all equations.

The cursor ( ! ) is visible while you are keying in a number or doing a

calculation. When the cursor is visible, pressing < deletes the last

character you keyed in. When the cursor is not visible, pressing <

erases the last number.

Keys: Display: Description:

12345 <<

.66

#$%&''!"

Backspacing removes

the 4 and 5.

@t (&(#" Calculates 1/123.66.

< (&((" Clears the calculator

line.

In addition, there are more drastic clearing operations that erase more

information at once. Refer to “Resetting the Calculator” on page 228 in

appendix A.

1: Getting Started 21

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Doing Arithmetic

The “

” in the margin is a reminder that the example keystrokes are

for ALG mode.

This is a brief introduction to doing arithmetic. More information on

arithmetic is in chapter 2. Remember that you can erase errors by

pressing < or C.

To calculate 21.1 ＋ 23.8:

Keys: Display: Description:

21.1 + $#&#()"

23.8 $#&#()$%&*"

= ++&,(" = completes calculation.

Once a calculation has been completed, pressing another digit key

starts a new calculation. On the other hand, pressing an operator key

continues the calculation:

77.35 - --&%./" Calculates 77.35 – 90.89

90.89 = /#%&.+"

65 @v* 12

,'&-."

New calculation:

65 x 12.

/ 3.5 = $-&'+" Calculates 96.75 ÷ 3.5.

You can also do long calculations without pressing = after each

intermediate calculation—just press it at the end. The operators perform

from left to right, in the order you enter them. Compare:

65 + 12 12

and 65 +

3.5 3.5

65 + 12 /

3.5 =

$$&(("

Operations occur in the

order you see them.

22 1: Getting Started

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65 +( 12 /

3.5 )=

'*&+%"

Use parentheses to impose

an order of calculation.

Keying in Negative Numbers (&)

The & key changes the sign of a number.

! To key in a negative number, type that number, then press &.

! To change the sign of an already displayed number (it must be the

rightmost number), press &.

Keys: Display: Description:

75 & /-." Changes the sign of 75.

* 7.1 = /.%$&.(" Multiplies －75 by 7.1.

Using the Menu Keys

The calculator usually displays a set of labels across the bottom of the

display. The set is called a menu because it presents you with choices.

The MAIN menu is the starting point for all other menus.

1: Getting Started 23

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()

Menu Ke

Menu Labels

The top row of keys is related to the labels along the bottom of the

display. The labels tell you what the keys do. The six keys are called

menu keys; the labels are called menu labels.

The MAIN Menu

The MAIN menu is a set of primary choices leading to other menu

options. No matter which menu you currently see, pressing @A

redisplays the MAIN menu. The menu structure is hierarchical.

24 1: Getting Started

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Table 1-3. The MAIN Menu

Menu Label Operations Done in

This Category Covered in:

TVM: Time value of money:

loans, savings, leasing,

amortization.

Chapter 5

ICNV: Interest conversions. Chapter 6

CFLO: Lists of cash flows for

internal rate of return and

net present value.

Chapter 7

BOND: Yields and prices

for bonds.

Chapter 8

" #

(Finance)

DEPRC: Depreciation using

SL, DB, and SOYD methods,

or ACRS.

Chapter 9

# #

(Business Percentages)

Percent of total, percent

change, markup on cost,

markup on price.

Chapter 3

$ !

(Statistics)

Lists of numbers, running

total, mean, weighted

statistics, forecasting,

summation statistics, and

more.

Chapter 10

% #

(Time Manager)

Clock, calendar,

appointments, date

arithmetic.

Chapter 11

& !

(Equation Solver)

Creates customized menus

from your own equations for

calculations you do often.

Chapter 12

' !

(Currency Exchange)

Converting any currency to

its equivalent in another

currency

Chapter 4

1: Getting Started 25

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Choosing Menus and Reading Menu Maps

Below is a menu map illustrating one possible path through three levels

of menus: from the MAIN menu to the BUS menu to the MU%C (markup

as a percent of cost) menu. There are no menus that branch from the

MU%C menu because the MU%C menu is a final destination―you

use it to do calculations, rather than to choose another menu.

FIN

%CHG

BUS

%TOTL

SUM

MU%C

TIME

MU%P

SOLVE CURRX

M%CPRICECOST

MAIN menu

BUS menu

MU%C menu

EXIT

EXIT MAIN

! Press

# to choose the BUS menu. Then press ( to choose

the MU%C menu.

! Press e to return to the previous menu. Pressing e enough

times returns you to the MAIN menu.

! Press

@A to return to the MAIN menu directly.

When a menu has more than six labels, the label ) appears at the

far right. Use it to switch between sets of menu labels on the same

“level”.

Example: Using Menus. Refer to the menu map for MU%C (above)

along with this example. The example calculates the percent markup on

cost of a crate of oranges that a grocer buys for $4.10 and sells for

$4.60.

Step 1. Decide which menu you want to use. The MU%C (markup as

a percent of cost) menu is our destination. If it’s not obvious

to you which menu you need, look up the topic in the subject

26 1: Getting Started

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index and examine the menu maps in appendix C.

Displaying the MU%C menu:

Step 2. To display the MAIN menu, press @A. This step lets you

start from a known location on the menu map.

Step 3. Press # to display the BUS menu.

Step 4. Press ( to display the MU%C menu.

Using the MU%C menu:

Step 5. Key in the cost and press ) to store 4.10 as the COST.

Step 6. Key in the price and press * to store 4.60 as the

PRICE.

Step 7. Press + to calculate the markup as a percent of cost.

The answer: 012345678#$&$(.

Step 8. To leave the MU%C menu, press e twice (once to get

back to the BUS menu, and again to get to the MAIN menu)

or @A (to go directly to the MAIN menu).

1: Getting Started 27

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Calculations Using Menus

Using menus to do calculations is easy. You don’t have to remember in

what order to enter numbers and in what order results come back.

Instead, the menus guide you, as in the previous example. All the keys

you need are together in the top row. The menu keys both store numbers

for the calculations and start the calculations.

The MU%C menu can calculate M%C, the percent markup on cost,

given COST and PRICE.

COST PRICE M%C

Calculator

Memory

Store 4.60

Store 4.10

Calculate 12.20

Keys: 4.60

Display:

Keys: 4.10

Display:

Keys:

Display:

Then the same menu can calculate PRICE given COST and M%C.

COST PRICE M%C

Calculator

Memory

Store 20.00

Store 4.10

Calculate 4.92

Keys: 20

Display:

Keys: 4.10

Display:

Keys:

Display:

Notice that the two calculations use the same three variables; each

variable can be used both to store and calculate values. These are

called built-in variables, because they are permanently built into the

calculator.

28 1: Getting Started

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Many menus in this calculator work like the example above. The rules

for using variables are:

! To store a value, key in the number and press the menu key.∗†

Arithmetic calculations, as well as single values, can be stored.

! To calculate a value, press the menu key without first keying in a

number. The calculator displays 7197491:;<=> when a value is

being calculated.

! To verify a stored value, press R (recall) followed by the menu

key. For example, R ) displays the value stored in COST.

! To transfer a value to another menu, do nothing if it is displayed

(that is, it is in the calculator line). A number in the calculator line

remains there when you switch menus. To transfer more than one

value from a menu, use storage registers. See page 45, “Storing and

Recalling Numbers.”

Exiting Menus (e)

The e key is used to leave the current menu and go back to the

previously displayed menu (as shown in the previous example). This is

true for menus you might pick by accident, too: e gets you out.

Clearing Values in Menus

The @c key is a powerful feature to clear all the data in the

currently displayed menu, giving you a clean slate for new calculations.

! If the current menu has variables (that is, if the display shows menu

labels for variables, such as COST, PRICE, and M%C in the MU%C

menu), pressing @c clears the values of those variables to

zero.

* If you have just switched menus and want to store the result already in the

calculator line, then you should press s before the menu key

† To store the same number into two different variables, use s for the second

variable, e.g. 25 * s )

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! If the current menu has a list (SUM, CFLO, or Solver), pressing

@c clears the values in the list.

To see what value is currently stored in a variable, press R menu

label.

Solving Your Own Equations (SOLVE)

This chapter has introduced some of the built-in menus the calculator

offers. But if the solution to a problem is not built into HP 17bII+, you

can turn to the most versatile feature of all: the Equation Solver. Here

you define your own solution in terms of an equation. The Solver then

creates a menu to go with your equation, which you can use over and

over again, just like the other menus in the calculator.

The Solver is covered in chapter 12, but here is an introductory example.

Because equations usually use letters of the alphabet, this section also

explains how to type and edit letters and other characters that aren’t on

the keyboard.

Example:Using the Solver. Suppose you frequently buy carpet and

must calculate how much it will cost. The price is quoted to you per

square yard. Regardless of how you do the calculation (even if you do it

longhand), you are using an equation.

×× =

P/YD L W COST

To type this equation into the Solver, use the ALPHA menu.

Price per

square yard Len

th (feet)

Converts square feet to square yards

Width (feet)

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Typing Words and Characters: the ALPHAbetic Menu

The ALPHAbetic menu is automatically displayed when you need it to

type letters and characters. The ALPHA menu also includes characters

not found on the keyboard:

! Uppercase letters.

! Space.

! Punctuation and special characters.

! Non-English letters.

ABCDE FGHI JKLM

space OTHER OTHER

RS TUV

: < > # $ , . /

Alpha

NOPQ RSTUV WXYZ

FGHI

&! @

Letters,

space

OTHER

characters

To type a letter you need to press two keys; for example, 1 is produced

by the keystrokes , - .

Each letter menu has an . key for accessing punctuation and

non-English characters. The letter menus with just four letters (for

example, FGHI) include a space character ( ! ).

To familiarize yourself with the ALPHA menu, type in the equation for the

cost of carpeting. The necessary keystrokes are shown below. (Note the

access to the special character, “/”.) Use <, if necessary, to make

corrections. If you need to do further editing, refer to the next section,

“Editing ALPHAbetic Text.” When you’re satisfied that the equation is

correct, press I to enter the equation into memory.

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Keys Characters

@A "

& / "

0 1 5"

2 . 3 4 5?"

2 5 , 6 5?@A"

* 7 8 * 5?@AB9B"

2 9 /9= 5?@AB9BCD,8"

, : 0 ; 5?@AB9BCD,87E"

< = < > 5?@AB9BCD,87EF:"

I 5?@AB9BCD,87EF:"

Note that the ? is just a character, part of the variable’s name. It is not

an operator, which ÷ is.

Editing ALPHAbetic Text

The companion to the ALPHA menu is the ALPHA-Edit menu. To display

the ALPHA-Edit menu, press * in the SOLVE menu (or press e

in the ALPHA menu).

DEL

ABCDE FGHI JKLM NOPQ RSTUV WXYZ

ALPHA EXIT

EXIT

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Table 1-4. Alphabetic Editing

Operation Label or Key to Press

ALPHA-Edit Menu

Inserts character before the cursor. Any character.

Deletes character at the cursor. ? !

Moves the cursor far left, one

display-width.

Moves the cursor left. A

Moves the cursor right. B

Moves the cursor far right, one

display-width.

Displays the ALPHA menu again. D

Keyboard

Backspaces and erases the character

before the cursor.

Clears the calculator line. C

Calculating the Answer (CALC)

After an equation is input, pressing E verifies it and creates a new,

customized menu to go with the equation.

Menu labels for your variables

Each of the variables you typed into the equation now appears as a

menu label. You can store and calculate values in this menu the same

way you do in other menus.

1: Getting Started 33

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Calculate the cost of carpet needed to cover a 9’ by 12’ room. The

carpet costs $22.50 per square yard.

Starting from the MAIN menu (press @A):

Keys: Display: Description:

& 5?@AB9BCD,87EF:" Displays the SOLVE menu

and the current

equation.*

E "Displays the customized

menu for carpeting.

22.5 "

5?@A 5?@A8$$&.(" Stores the price per

square yard in P/YD.

12 8 98#$&((" Stores the length in L.

9 9 C8,&((" Stores the width in W.

) 7EF:8$-(&((" Calculates the cost to

cover a 9’ x 12’ room.

Now determine the most expensive carpet you can buy if the maximum

amount you can pay is $300. Notice that all you need to do is enter the

one value you are changing―there is no need to re-enter the other

values.

300 ) 7EF:8%((&((" Stores $300 in COST.

5?@A" 5?@A8$.&((" Calculates the maximum

price per square yard you

can pay.

ee "Exits Solver.

* If you entered this equation but don’t see it now, press [ or ] until you do.

34 1: Getting Started

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Controlling the Display Format

The DSP menu (press D) gives you options for formatting numbers.

You can pick the number of decimal places to be displayed, and

whether to use a comma or a period to “punctuate” your numbers.

Decimal Places

To change the number of displayed decimal places, first press the D

key. Then either:

! Press

+ , type the number of decimal places you want (from 0 to

11), and press I; or

! Press

, to see a number as precisely as possible at any time

(12 digits maximum).

Internal Precision

Changing the number of displayed decimal places affects what you see,

but does not affect the internal representation of numbers. The number

inside the calculator always has 12 digits.

You see only these

its in 2...

...but these di

its are

also present internally.

Temporarily SHOWing ALL

To temporarily see a number with full precision, press @S.This

shows you the ALL format for as long as you hold down S.

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Rounding a Number

The @r function rounds the number in the calculator line to the

number of displayed decimal places. Subsequent calculations use the

rounded value.

Starting with two displayed decimal places:

Keys: Display: Description:

5.787 .&-*-!"

D +

4 I

.&-*-("

Four decimal places are

displayed.

D , .&-*-" All significant digits;

trailing zeros dropped.

D +

2 I

.&-,"

Two decimal places are

displayed.

(hold)

G499 52H7;F;E< ;FI"

.&-*-"

Temporarily shows full

precision.

@S (hold)

.&-,"

Rounds the number to two

decimal places.

Exchanging Periods and Commas in Numbers

To exchange the periods and commas used for the decimal point and

digit separators in a number:

1. Press D to access the DSP (display) menu.

2. Specify the decimal point by pressing F or G. Pressing

F sets a period as the decimal point and comma as the digit

separator (U.S. mode). (For example, 1,000,000.00.) Pressing

G sets a comma as the decimal point and period as the digit

separator (non-U.S. mode). (For example, 1.000.000,00.)

36 1: Getting Started

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Error Messages

Sometimes the calculator cannot do what you “ask”, such as when you

press the wrong key or forget a number for a calculation. To help you

correct the situation, the calculator beeps and displays a message.

! Press

C or < to clear the error message.

! Press any other key to clear the message and perform that key’s

function.

For more explanations, refer to the list of error messages just before the

subject index.

Modes

Beeper. Beeping occurs when a wrong key is pressed, when an error

occurs, and during alarms for appointments. You can suppress and

reactivate the beeper in the MODES menu as follows:

1. Press @>.

2. Pressing - will simultaneously change and display the cur-

rent setting for the beeper:

! JHH5H2 E< beeps for errors and appointments.

! JHH5H2 E<I 155:F E<9@ beeps only for appointments.

! JHH5H2 EGG silences the beeper completely.

3. Press e when done.

Print. Press @> . to specify whether or not the printer ac

adapter is in use. Then press e.

Double Space. Press @> / to turn double-spaced printing

on or off. Then press e.

Algebraic. Press @> 0 to select algebraic entry logic.

RPN. Press @> 1 to select Reverse Polish Notation entry

logic.

1: Getting Started 37

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Language. Press @> ! to change the language.

Calculator Memory (@M)

The calculator stores many different types of information in its memory.

Each piece of information requires a certain amount of storage space.*

You can monitor the amount of available memory by pressing @M.

Number of b

tes of

memor

still free Percenta

e of total

memor

still free

The amount of memory available for storing information and working

problems is about 30,740 bytes. (Units of memory space are called

bytes.) The calculator gives you complete flexibility in how you use that

available memory (such as for lists of numbers or equations). Use as

much of the memory as you want for any task you want.

If you use nearly all of the calculator’s memory, you’ll encounter the

message ;<F4GG;7;H<: 0H0E2@. To remedy this situation, you

must erase some previously stored information. Refer to “Managing

Calculator Memory” on page 227 in appendix A.

The calculator also allows you to erase at once all the information stored

inside it. This procedure is covered in “Erasing Continuous Memory” on

page 230.

* Storing numbers in menus like TVM (non-Solver menus) does not use any of

your memory space.

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Arithmetic

If you prefer RPN to algebraic logic, please read appendix D before

you read this chapter. The “ v “ in the margin is a reminder that the

example keystrokes are for ALG mode.

The Calculator Line

The calculator line is the part of the display where numbers appear and

calculations take place. Sometimes this line includes labels for results,

such as :E:198#$+&'(. Even in this case you can use the number

for a calculation. For example, pressing + 2 = would calculate

124.60 plus 2, and the calculator would display the answer, 126.60.

There is always a number in the calculator line, even though some-

times the calculator line is hidden by a message (such as FH9H7:

7E05E4<A;<=). To see the number in the calculator line, press <,

which removes the message.

Doing Calculations

Simple calculating was introduced in chapter 1, page 21. Often longer

calculations involve more than one operation. These are called chain

calculations because several operations are “chained” together. To do

a chain calculation, you don’t need to press = after each operation,

but only at the very end.

For instance, to calculate 750 12

360

× you can type either:

750 * 12 =/ 360 =

750 * 12 / 360 =

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In the second case, the / key acts like the = key by displaying the

result of 750 x 12.

Here’s a longer chain calculation.

456 - 75 68

18.5 1.9

This calculation can be written as: 456 − 75 ÷ 18.5 x 68 ÷ 1.9.

Watch what happens in the display as you key it in:

Keys: Display:

456 - 75 / %*#&((D"

18.5 * $(&.,B"

68 / #K+((&+%D"

1.9 = -%-&(-"

Using Parentheses in Calculations

Use parentheses when you want to postpone calculating an

intermediate result until you’ve entered more numbers. For example,

suppose you want to calculate:

30 x 9

85 -12

If you were to key in 30 / 85 -, the calculator would calculate the

intermediate result, 0.35. However, that’s not what you want. To de-

lay the division until you’ve subtracted 12 from 85, use parentheses:

Keys: Display: Description:

30 /( 85- %(&((DL*.&((/" No calculation is done.

12 ) %(&((D-%&((" Calculates 85 − 12.

* 9 (&+#B," Calculates 30 / 73.

= %&-(" Calculates 0.41x 9.

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Note that you must include a * for multiplication; parentheses do not

imply multiplication.

The Percent Key

The% key has two functions:

Finding a Percentage. In most cases, % divides a number by 100.

The one exception is when a plus or minus sign precedes the number.

(See “Adding or Subtracting a Percentage,” below.)

For instance, 25 % results in (&$..

To find 25% of 200, press: 200 * 25 % =. (Result is .(&((.)

Adding or Subtracting a Percentage. You can do this all in one

calculation:

For instance, to decrease 200 by 25%, just enter 200 - 25 % =.

(Result is #.(&((.)

Example: Calculating Simple Interest. You borrow $1,250 from a

relative, and agree to repay the loan in a year with 7% simple interest.

How much money will you owe?

Keys: Display: Description:

1250 + 7 % #K$.(&(()*-&.(" Interest on the loan is

$87.50.

= #K%%-&.(" You must repay this

amount at the end of one

year.

The Mathematical Functions

Some of the math functions appear on the keyboard; others are in the

MATH menu. Math functions act on the last number in the display.

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Table 2-1. Shifted Math Functions

Key Description

@t reciprocal

@v square root

@w square

Keys: Display: Description:

4 @t (&$." Reciprocal of 4.

20 @v +&+-" Calculates 20 .

+ 47.2 * .#&'-B" Calculates 4.47 + 47.20.

1.1 @w .#&'-B#&$#" Calculates 1.12.

= '$&.$" Completes calculation of

(4.47 + 47.2) x1.12.

The Power Function (Exponentiation)

The power function, u, raises the preceding number to the power of

the following number.

Keys: Display: Description:

125 @u 3 = #K,.%K#$.&((" Calculates 1253.

125 @u 3

@t=

.&(("

Calculates the cube root of

125, which is the same as

(125)1/3.

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The MATH Menu

To display the MATH menu, press @m (the shifted % key). Like the

other mathematics functions, these functions operate on only the last

number in the display.

Table 2-2. The MATH Menu Labels

Menu Label Description

H !

Common (base 10) logarithm of a positive number.

2 #

Common (base 10) antilogarithm; calculates 10x.

3 Natural (base e) logarithm of a positive number.

I !

Natural antilogarithm; calculates ex.

4 Factorial.

5 Inserts the value for π into the display.

Keys: Display: Description:

2.5 @m

%#'&$%"

Calculates 102.5.

4 4" $+&((" Calculates the factorial of 4.

e "Exits MATH menu.

You can access the MATH menu when another menu is displayed. For

instance, while using SUM you might want to use a MATH function. Just

press @m, then perform the calculation. Pressing e returns you

to SUM. The MATH result remains in the calculator line. Remember,

however, that you must exit MATH before you resume using SUM.

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Saving and Reusing Numbers

Sometimes you might want to include the result of a previous calculation

in a new calculation. There are several ways to reuse numbers.

The History Stack of Numbers

When you start a new operation, the previous result moves out of the

display but is still accessible. Up to four lines of numbers are saved: one

in the display and three hidden. These lines make up the history stack.

"Invisible"

numbers

remainin

from

revious results.

The ], [, and @~ keys “roll” the history stack down or up one line,

bringing the hidden results back into the display. If you hold down

[ or ], the history stack wraps around on itself. However, you

cannot roll the history stack when an incomplete calculation is in the

display. Also, you cannot gain access to the stack while using lists

(SUM, CFLO) in ALG mode, or SOLVE in either ALG or RPN mode. All

numbers in the history stack are retained when you switch menus.

Pressing @x exchanges the contents of the bottom two lines of the

display.

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Pressing @c clears the history stack. Be careful if a menu is

active, because then c also erases the data associated with that

menu.

Keys: Display: Description:

75.55 - 32.63

+$&,$"

150 / 7 = $#&+%" 42.92 moves out of

display.

Now, suppose you want to multiply 42.92 x 11. Using the history stack

saves you time.

] +$&,$" Moves 42.92 back to

calculator line.

* 11 = +-$&#$"

Reusing the Last Result (@L)

The @L key copies the last result―that is, the number just above

the calculator line in the history stack―into a current calculation.

This lets you reuse a number without retyping it and also lets you break

up a complicated calculation.

39 8

123 17

Keys: Display: Description:

123 + 17 = #+(&((" Calculates 123 + 17.

@ v ##&*%" Calculates 140 .

39 + 8 =/

+-&((D##&*%"

Copies 11.83 to the

calculator line.

= %&,-" Completes the calculation.

2: Arithmetic 45

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An equivalent keystroke sequence for this problem would be:

39 + 8 / (123 + 17 ) @v =

Storing and Recalling Numbers

The s key copies a number from the calculator line into a

designated storage area, called a storage register. There are ten

storage registers in calculator memory, numbered 0 through 9. The

R key recalls stored numbers back to the calculator line.

lf there is more than one number on the calculator line, s stores only

the last number in the display.

To store or recall a number:

1. Press s or R. (To cancel this step, press <.)

2. Key in the register number.

The following example uses two storage registers to do two calculations

that use some of the same numbers.

475.6 560.1 + 475.6

39.15 39.15

Keys: Display: Description:

475.6 s 1 +-.&'(" Stores 475.6 into register

/ 39.15 s

+-.&'(D%,&#."

Stores 39.15 (rightmost

number) into register 2.

= #$&#." Completes calculation.

560.1 +R

.'(&#()+-.&'("

Recalls contents of register

/R 2 #K(%.&-(D%,&#." Recalls register 2.

= $'&+." Completes calculation.

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The s and R keys can also be used with variables. For example,

s + (in the MU%C menu) stores the rightmost number from the

display into the variable M%C. R + copies the contents of

M%C into the calculator line. If there is an expression in the display

(such as $)+!), then the recalled number replaces only the last

number.

You do not need to clear storage registers before using them. By storing

a number into a register, you overwrite whatever existed there before.

Doing Arithmetic Inside Registers and Variables

You can also do arithmetic inside storage registers.

Keys: Display: Description:

45.7 s 3 +.&-(" Stores 45.7 in reg. 3.

2.5 s* 3 $&.(" Multiplies contents of

result (114.25) back in

R 3 ##+&$." Displays register 3.

Table 2-3. Arithmetic in Registers

Keys New Register Contents

s+ old register contents + displayed number

s- old register contents – displayed number

s* old register contents x displayed number

s/ old register contents ÷ displayed number

s@u old register contents ^ displayed number

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You can also do arithmetic with the values stored in variables. For

example, 2 s* + (in the MU%C menu) multiplies the current

contents of M%C by 2 and stores the product in M%C.

Scientific Notation

Scientific notation is useful when working with very large or very small

numbers. Scientific notation shows a small number (less than 10) times

10 raised to a power. For example, the 1984 Gross National Product of

the United States was $3,662,800,000,000. In scientific notation, this is

3.6628 x1012. For very small numbers the decimal point is moved to the

right and 10 is raised to a negative power. For example, 0.00000752

can be written as 7.52 x 10−6.

When a calculation produces a result with more than 12 digits, the

number is automatically displayed in scientific notation, using a capital

E in place of “x10^”.

Remember that & changes the sign of the entire number, and not of

the exponent. Use - to make a negative exponent.

Type in the numbers 4.78 x 1013 and −2.36 x 10−15.

Keys: Display: Description:

4.78 @\ 13 +&-*H#%" Pressing @\ starts the

exponent.

@c (&((" Clears number.

2.36 @\-

$&%'H/#."

Pressing - before an

exponent makes it

negative.

& /$&%'H/#." Pressing & makes the

entire number negative.

@c "Clears number.

48 2: Arithmetic

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Range of Numbers

The largest positive and negative numbers available on the calculator

are ±9.99999999999 x 10 499; the smallest positive and negative

numbers available are ±1 x 10 –499.

3: Percentage Calculations in Business 49

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Percentage Calculations

in Business

The business percentages (BUS) menu is used to solve four types of

problems. Each type of problem has its own menu.

FIN

%CHG

BUS

%TOTL

SUM

MU%C

TIME

MU%P

SOLVE CURRX

Table 3-1. The Business Percentages (BUS) Menus

Menu Description

Percent change

( J )

The difference between two numbers (OLD and

NEW), expressed as a percentage (%CH) of

OLD.

Percent of total

( K )

The portion that one number (PART) is of another

(TOTAL), expressed as a percentage (%T).

Markup on cost

( ( )

The difference between price (PRICE) and cost

(COST), expressed as a percentage of the cost

(M%C).

Markup on price

( L )

The difference between price (PRICE) and cost

(COST), expressed as a percentage of the price

(M%P).

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The calculator retains the values of the BUS variables until you clear

them by pressing @c. For example, pressing @c while in

the %CHG menu clears OLD, NEW, and %CH.

To see what value is currently stored in a variable, press R menu

label. This shows you the value without recalculating it.

Using the BUS Menus

Each of the four BUS menus has three variables. You can calculate any

one of the three variables if you know the other two.

1. To display the %CHG, %TOTL, MU%C, or MU%P menu from the

MAIN menu, press #, then the appropriate menu label. Pressing

J, for example, displays:

2. Store each value you know by keying in the number and pressing the

appropriate menu key.

3. Press the menu key for the value you want to calculate.

Examples Using the BUS Menus

Percent Change (%CHG)

Example. Total sales last year were $90,000. This year, sales were

$95,000. What is the percent change between last year’s sales and this

year’s?

Keys: Display: Description:

# J "Displays %CHG menu.

3: Percentage Calculations in Business 51

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90000 M E9A8,(K(((&(("Stores 90,000 in OLD.

95000 / <HC8,.K(((&((" Stores 95,000 in NEW.

N !67M1<=H8.&.'" Calculates percent

change.

What would this year’s sales have to be to show a 12% increase from

last year? OLD remains 90,000, so you don’t have to key it in again.

Just enter %CH and ask for NEW.

12 N 67M1<=H8#$&((" Stores 12 in %CH.

/ <HC8#((K*((&((" Calculates the value 12%

greater than 90,000.

Percent of Total (%TOTL)

Example. Total assets for your company are $67,584, The firm has

inventories of $23,457. What percentage of total assets is inventory?

You will be supplying values for TOTAL and PART and calculating %T.

This takes care of all three variables, so there is no need to use c

to remove old data.

Keys: Display: Description:

# K "Displays %TOTL menu.

67584 O :E:198'-K.*+&((" Stores $67,584 in TOTAL.

23457 P 512:8$%K+.-&((" Stores $23,457 in PART.

Q 6:E:198%+&-#" Calculates percent of

total.

52 3: Percentage Calculations in Business

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Markup as a Percent of Cost (MU%C)

Example. The standard markup on costume jewelry at Balkis’s Boutique

is 60%. The boutique just received a shipment of chokers costing

$19.00 each. What is the retail price per choker?

Keys: Display: Description:

# ( "Displays MU%C menu.

19 ) 7EF:8#,&((" Stores cost in COST.

60 + 012345678'(&((" Stores 60% in M%C.

* 52;7H8%(&+(" Calculates price.

Markup as a Percent of Price (MU%P)

Example. Kilowatt Electronics purchases televisions for $225, with a

discount of 4%. The televisions are sold for $300. What is the markup

of the net cost as a percent of the selling price?

What is the markup as percent of price without the 4% discount?

Keys: Display: Description:

# L "Displays MU%P menu.

225 - 4 %

)

7EF:8$#'&(("

Calculates and stores net

cost in COST.

300 * 52;7H8%((&((" Stores 300 in PRICE.

6 012345658$*&((" Calculates markup as a

percent of price.

Use $225 for COST and leave PRICE alone.

225 ) 7EF:8$$.&((" Stores 225 in COST.

6 012345658$.&((" Calculates markup.

3: Percentage Calculations in Business 53

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Sharing Variables Between Menus

If you compare the MU%C menu and the MU%P menus, you’ll see that

they have two menu labels in common –– ) and *.

COST

Shared variables

%CHG

PRICE

%TOTL

M%C

M%P

MU%C MU%P

The calculator keeps track of the values you key in according to those

labels. For example, if you key in COST and PRICE in the MU%C menu,

exit to the BUS menu, and then display the MU%P menu, the calculator

retains those values. In other words, the variables are shared between

the two menus.

Example: Using Shared Variables. A food cooperative buys cases of

canned soup with an invoice cost of $9.60 per case. If the co-op

routinely uses a 15% markup on cost, for what price should it sell a case

of soup?

Keys: Display: Description:

# ( "Displays MU%C menu.

9.6 ) 7EF:8,&'(" Stores 9.60 in COST.

15 + 012345678#.&((" Stores 15% in M%C.

* 52;7H8##&(+" Calculates retail price.

What is the markup on price? Switch menus but keep the same COST

and PRICE.

e L "Exits MU%C menu and

displays MU%P menu.

6 012345658#%&(+" Calculates markup as a

percent of price.

54 4: Currency Exchange Calculation

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Currency Exchange

Calculations

The CURRX menu does currency exchange calculations between two

currencies using an exchange rate that you calculate or store.

The CURRX Menu

BUSFIN SUM TIME SOLVE CURRX

SELCT

US$ EUR RATE C.STO C.RCL

To display the currency exchange menu from the MAIN menu, press

' .

Currenc

#2 is EUR

(EURO Dollar)

Currenc

#1 is US$

(U.S Dollar)

4: Currency Exchange Calculation 55

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Table 4–1. The CURRX Menu

Menu Key Description

Curr1 Current currency#1;stores or calculates the number of units

of this currency

Curr2 Currency currency#2;stores or calculates the number of

units of this currency

7 #

Stores or calculates the exchange rate between the two

current currencies. The rate is expressed as the number of

units of currency #2 equivalent to 1 unit of currency #1.

8 Stores the current currency #1, currency #2, and RATE.

9 Recalls a previously stored pair of currencies and RATE.

: Selects a new set of currencies.

Selecting a Set of Currencies

To select a pair of currencies:

1. Press : to display the menu of currencies. Press more, if

necessary, to see additional currencies ( see table 4–2 ).

2. Press a menu key to select currency #1.

3. Press a menu key to select currency #2. RATE is automatically reset to

1.0000.

4. Enter an exchange rate. There are two ways enter the RATE :

! Calculate the rate from a known equivalency (see the

example ”Calculating an Exchange Rate,” page 57.). Calculating an

exchange rate is usually the easier way to enter a correct rate, since

the order in which you selected the two currencies doesn’t mater.

! Store the exchange rate by keying in the value and pressing (see

“Storing an Exchange Rate” on page 58).

56 4: Currency Exchange Calculation

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Table 4–2. Currencies

; #< ## = #> "

United States

of America

(Dollars)

Austria,

Belgium,

Germany,

Spain,

Finland,

France,

Greece,

Ireland, Italy,

Luxembourg,

Netherlands,

Portugal,

Vatican City

(EURO)

Canada

(Dollars)

United Kingdom

(Pounds)

? #

@ #A #B #C #

Switzerland

(Francs)

Israeli

(New

Shekel)

Denmark

(Kroner)

Norway

(Kroner)

Sweden

(Kronor)

R !

D #E #F #G #

Russia

(Rouble)

South Africa

(Band)

Saudi Arabia

(Riyals)

Argentina Vanuatu

(Bolivar)

Brazil Peru

H #I #J #K #L #

Bolivia Chile,

Colombia,

Mexico,

Philippines,

Uruguay

(Pesos)

Hong Kong

(Dollars)

Taiwan

(New Dollars)

China

(Yuan

Renminbi)

South Korea

(Won)

M #"

1N" #N #O # P #

Japan

(Yen)

Australia

(Dollars)

Malaysia

(Ringgits)

New Zealand

(Dollars)

Indonesia

(Rupiahs)

Q #R #S #T #U

Singapore

(Dollars)

Thailand

(Baht)

India

(Rupee)

Pakistani

(Rupees)

Miscellaneous*

* Use for currencies not shown in table

4: Currency Exchange Calculation 57

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Entering a Rate

The following two examples illustrate the two ways to enter an exchange

rate.

Example: Calculating an Exchange Rate. You have just flown from

Canada to United States, and you need to exchange your Canadian

Dollars for U.S Dollars. The conversion chart looks this :

United States Conversion Chart (in US$)

Currency Rate

Euro (EUR€) 1.0842

Canadian (CAN$) .6584

Hong Kong (HK$) .1282

The chart states these equivalencies: *

1 EUR€ is equivalent to 1.0842 US$

1 CAN$ is equivalent to 0.6584 US$

1 HK$ is equivalent to 0.1282 US$

Part 1: Select the currencies, and calculate an exchange rate form them.

Keys: Display: Description:

' !H<:H2 1 21:H" Display the CURRX menu

: = "FH9H7: 7422H<7@ $" Select CAN$ as currency

; H<:H2 1 21:H" Select US$ as currency #2

1 = 71<N8#&((" Store number of CAN$

* The chart is in terms of United States dollars. Many charts have two columns–a

“Buy” column and a “Sell” column. The “Buy” column is used for transactions

in which the “Bank” buys the listed currency from you in exchange for United

States dollars. Thus, if you arrive in United States with CAN$, the exchange

rate in the “Buy” column applies for buying US$ with your CAN$. The “Sell”

column applies for selling US$ in exchange for CAN$.

58 4: Currency Exchange Calculation

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0.6584 ; 4FN8(&''" Stores equivalent number

of US$

7 21:H8(&''" Calculates the RATE.

Part 2: The following keystrokes show that you can reverse the order in

which the two currencies are selected.

Keys: Display: Description:

: ; FH9H7: 7422H<7@ $" Select US$ as currency #1

= H<:H2 1 21:H" Select CAN$ as currency

1 = 71<N8#&((" Store number of CAN$

0.6584 ; 4FN8(&''" Stores equivalent number

of US$

7 21:H8#&.$" Calculates the RATE.

(1 ÷ 0.6584 )

Example : Storing an Exchange Rate. If you choose to store the

exchange rate directly, you must select the currencies in the correct order,

since the RATE is defined as the number of units of currency #2

equivalent to one unit of currency#1

Use the United States conversion chart on page 57 to store an exchange

rate for converting between Hong Kong Dollars and U.S. Dollars.

Keys: Display: Description:

' !H<:H2 1 21:H" Display the CURRX menu

: 3 #

3 3

FH9H7: 7422H<7@ $"

Select HK$ as currency

; H<:H2 1 21:H" Select US$ as currency #2

0.1282 7 21:H8(&#%" Store the RATE

4: Currency Exchange Calculation 59

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Converting Between Two Currencies

Once the currencies are selected and a RATE has been entered, you can

convert any number of units of one currency to the other.

Example : Converting between Hong Kong and U.S Dollars.

Part 1: Use the exchange rate stored in the previous example to

calculate how many U.S dollars you would receive for 3,000 Hong

Kong Dollars.

Keys: Display: Description:

3000 I M3N8%K(((&((" Store number of HK$

; 4FN8%*+&'(" Calculates equivalent US$

Part 2: A wool sweater in a shop window costs 75 US$. What is its cost

in HK$ Dollars?

Keys: Display: Description:

75 ; 4FN8-.&((" Store number of US$

I M3N8.*.&($" Calculates equivalent HK$

Storing and Recalling Sets of Currencies

Pressing 8 or 9 displays the C.STO/C.RCL menu, which is

used to store and recall sets of currencies and the rates. The menu can

store up to six sets of currencies. Initially, the menu contains six blank

labels.

Storing Sets of Currencies. To store the current set of currencies and the

rate, press. Then, press 8 any menu key to assign the set to that

key. For example, storing the currencies in the previous example stores

currency #1 = HK$, currency #2 = US$, and RATE = 0.1282. ( The

values US$ = 75 and HK$ = 585.02 are not stored.)

60 4: Currency Exchange Calculation

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Recalling Sets of Currencies. To recall a stored set of currencies and

their exchange rate, press 9 , followed by the appropriate menu

key. The HP 17bII+ automatically returns to the CURRX menu. The

equivalency message and menu labels show the recalled currencies and

RATE.

Clearing the Currency Variables

Pressing @c while the CURRX menu is displayed sets the RATE to

1.0000. The values of the two current currencies are cleared to 0.

5: Time Value of Money 61

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Time Value of Money

The phrase time value of money describes calculations based on money

earning interest over a period of time. The TVM menu performs

compound-interest calculations and calculates (and prints) amortization

schedules.

! In compound interest calculations, interest is added to the principal at

specified compounding periods, thereby also earning interest.

Savings accounts, mortgages, and leases are compound-interest

calculations.

! In simple interest calculations, the interest is a percent of the principal

and is repaid in one lump sum. Simple interest calculations can be

done using the % key (page 40). For an example that calculates

simple interest using an annual interest rate, see page 190.

The TVM Menu

FIN BUS SUM TIME

TVM

I%YR

BEG

P/YR

ICNV

END

CFLO

PMT

BOND

DEPRC

OTHER

AMRT

SOLVE CURRX

62 5: Time Value of Money

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The time value of money (TVM) menu does many compound-interest

calculations. Specifically, you can use the TVM menu for a series of cash

flows (money received or money paid) when:

! The dollar amount is the same for each payment.*

! The payments occur at regular intervals.

! The payment periods coincide with the compounding periods.

Payment mode: the

end of each period

12 payments (or periods)

per year

To second level of TVM

Figure 5-1. The First Level of TVM

The first level of the TVM menu has five menu labels for variables plus

.. The . key accesses a second-level menu used to specify

payment conditions (the payment mode) and to call up the AMRT

(amortization) menu.

Figure 5-2. The Second Level of TVM

* For situations where the amount of the payment varies, use the CFLO (cash

flows) menu.

5: Time Value of Money 63

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Table 5-1. TVM Menu Labels

Menu Label Description

First Level

S !

Stores (or calculates) the total number of payments or

compounding periods.*† (For a 30-year loan with

monthly payments, N＝12 x 30＝360.)

@ T Shortcut for N: Multiplies the number in the display by

P/YR, and stores the result in N. (If P/YR were 12, then

30 @ T would set N＝360.)

U Stores (or calculates) the nominal annual interest rate

as a percentage.

V Stores (or calculates) the present value―an initial cash

flow or a discounted value of a series of future cash

flows (PMTs + FV). To a lender or borrower, PV is the

amount of the loan; to an investor, PV is the initial

investment. If PV paid out, it is negative. PV always

occurs at the beginning of the first period.

W Stores (or calculates) the dollar amount of each periodic

payment. All payments are equal, and no payments are

skipped. (If the payments are unequal, use CFLO, not

TVM.) Payments can occur at the beginning or end of

each period. If PMT represents money paid out, it is

negative.

Stores (or calculates) the future value―a final cash

flow or a compounded value of a series of previous

cash flows (PV + PMTs). FV always occurs at the end of

the last period. If FV is paid out, it is negative.

. e

Second Level

Y Specifies the number of payments or compounding

periods per year.† (it must be an integer, 1 through

999.)

* When a non-integer N (an “odd period”) is calculated, the answer must be

interpreted carefully. See the savings account example on page 71.

Calculations using a stored, non-integer N produce a mathematically

correct result, but this result has no simple interpretation. The example on

page 172 uses the Solver to do a partial-period (non-integer) calculation in

which interest begins to accrue prior to the beginning of the first regular

payment period.

† The number of payment periods must equal the number of compounding periods. If

this is not true, see page 87. For Canadian mortgages, see page 197.

64 5: Time Value of Money

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Table 5-1. TVM Menu Labels (Continued)

Menu Label Description

Second Level (Continued)

Z !

Sets Begin mode: payments occur at the beginning of

each period. Typical for savings plans and leasing.

(The Begin and End modes do not matter if PMT＝0.)

[ Sets End mode: payments occur at the end of each

period. Typical for loans and investments.

\ Accesses the amortization menu. See page 78.

The calculator retains the values of the TVM variables until you clear

them by pressing @c. When you see the first-level TVM menu,

pressing @c clears N, I%YR, PV, PMT, and FV.

When the second-level menu ( . ) is displayed, pressing

@c resets the payment conditions to #$ 5?@2 H<A 0EAH.

To see what value is currently stored in a variable, press R menu

label. This shows you the value without recalculating it.

Cash Flow Diagrams and Signs of Numbers

It is helpful to illustrate TVM calculations with cash-flow diagrams.

Cash-flow diagrams are time lines divided into equal segments called

compounding (or payment) periods. Arrows show the occurrence of

cash flows (payments in or out). Money received is a positive number

(arrow up) and money paid out is a negative number (arrow down).

The correct sign (positive or negative) for TVM numbers is

essential. The calculations will make sense only if you

consistently show payments out as negative and payments in

Note

5: Time Value of Money 65

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(receipts) as positive. Perform a calculation from the point of view of

either the lender (investor) or the borrower, but not both!

12345

PMT

ual

eriods

ual

ments

(FV is

Future Value,

if an

; e.

a balloon

ment)

Mone

re-

ceived is a

ositive

number

Mone

aid out

is a ne

ative

number

(Loan)

Figure 5-3. A Cash Flow Diagram for a Loan from Borrower’s

Point of View (End Mode)

12345

Loan

Figure 5-4. A Cash Flow Diagram for a Loan from Lender’s

Point of View (End Mode)

66 5: Time Value of Money

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Payments occur at either the beginning of each period or the end of

each period. End mode is shown in the last two figures; Begin mode is

shown in the next figure.

12345

italized

value

of lease

Figure 5-5. Lease Payments Made at the Beginning of Each

Period (Begin Mode)

Using the TVM Menu

First draw a cash-flow diagram to match your problem. Then:

1. From the MAIN menu, press " ].

2. To clear previous TVM values, press @c, (Note:You don’t

need to clear data if you enter new values for all five variables, or if

you want to retain previous values.)

3. Read the message that describes the number of payments per year

and the payment mode (Begin, End). If you need to change either of

these settings, press ..

! To change the number of payments per year, key in the new value

and press Y. (If the number of payments is different from the

number of compounding periods, see “Compounding Periods

Different from Payment Periods,” page 87.)

! To change the Begin/End mode, press Z or [

! Press

e to return to the primary TVM menu.

5: Time Value of Money 67

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4. Store the values you know. (Enter each number and press its menu

key.)

5. To calculate a value, press the appropriate menu key.

You must give every variable―except the one you will calculate―a

value, even if that value is zero. For example, FV must be set to zero

when you are calculating the periodic payment (PMT) required to

fully pay back a loan. There are two ways to set values to zero:

! Before storing any TVM values, press @c to clear the previous

TVM values.

! Store zero; for example, pressing 0 X sets FV to zero.

Loan Calculations

Three examples illustrate common loan calculations. (For amortization of

loan payments, see page 77.) Loan calculations typically use End mode

for payments.

Example:A Car Loan. You are financing the purchase of a new car with

a 3-year loan at 10.5% annual interest, compounded monthly. The

purchase price of the car is $7,250. Your down payment is $1,500.

What are your monthly payments? (Assume payments start one month

after purchase ― in other words, at the end of the first period.) What

interest rate would reduce your monthly payment by $10?

1235 36

3 12

10.5

12; End mode

7, 2 5 0 _ 1,500

68 5: Time Value of Money

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Keys: Display: Description:

" ] "Displays TVM menu.

@c #$ 5?@2 H<A 0EAH" Clears history stack and

TVM variables.

#$ 5?@2 H<A 0EAH"

If needed: sets 12

payment periods per year;

End mode.

3 * 12

<8%'&(("

Figures and stores number

of payments.

10.5 U ;6@28#(&.(" Stores annual interest rate.

7250 - 1500

5O8.K-.(&(("

Stores amount of the loan.

W 50:8/#*'&*," Calculates payment.

Negative value means

money to be paid out.

To calculate the interest rate that reduces the payment by $10, add 10

to reduce the negative PMT value.

+ 10 W 50:8/#-'&*," Stores the reduced

payment amount.

U ;6@28'&-." Calculates the annual

interest rate.

Example: A Home Mortgage. After careful consideration of your

personal finances, you’ve decided that the maximum monthly mortgage

payment you can afford is $630. You can make a $12,000 down

payment, and annual interest rates are currently 11.5%. If you take out

a 30-year mortgage, what is the maximum purchase price you can

afford?

5: Time Value of Money 69

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1 2 359 360

_630

30 12

11.5

12; End mode

Keys: Display: Description:

" ] !

"Display TVM menu.

@c #$ 5?@2 H<A 0EAH" Clears history stack and

TVM variables.

. @c

#$ 5?@2 H<A 0EAH"

If needed: sets 12 payment

periods per year; End

mode.

30 @ T M8%'(&((" Pressing @ first multiplies

30 by 12, then stores this

number of payments in N.

11.5 U ;6@28##&.(" Stores annual interest rate.

630 &

50:8/'%(&(("

Stores a negative monthly

payment.

V 5O8'%K'#-&'+" Calculates loan amount.

+ 12000 = -.K'#-&'+" Calculates total price of the

house (loan plus down

payment).

Example: A Mortgage with a Balloon Payment. You’ve taken out a

25-year, $75,250 mortgage at 13.8% annual interest. You anticipate

that you will own the house for four years and then sell it, repaying the

loan in a “balloon payment.” What will be the size of your balloon

payment?

70 5: Time Value of Money

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12 4748

Balloon.

4 12

13.8

12; End mode

75,250

The problem is done in two steps:

1. Calculate the monthly payment without the balloon (FV=0).

2. Calculate the balloon payment after 4 years.

Keys: Display: Description:

" ] "Display TVM menu.

@c #$ 5?@2 H<A 0EAH" Clears history stack and

TVM variables.

. @c

#$ 5?@2 H<A 0EAH"

If needed: sets 12 payment

periods per year; End

mode.

Step 1. Calculate PMT for the mortgage.

25 @ T <8%((&((" Figures and stores the

number of monthly

payments in 25 years.

13.8 U ;6@28#%&*(" Stores annual interest rate.

75250 V 5O8-.K$.(&((" Stores amount of the loan.

W 50:8/*,+&%%" Calculates monthly

payment.

5: Time Value of Money 71

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Step 2. Calculate the balloon payment after 4 years.

894.33 &

50:8/*,+&%%"

Stores rounded PMT value

for exact payment amount

(no fractional cents).*

4 @ T <8+*&((" Figures and stores number

of payments in 4 years.

X 5O8/-%K+(*&*#" Calculates balloon payment

after four years. This

amount plus last monthly

payment repays the loan.

Savings Calculations

Example: A Savings Account. You deposit $2,000 into a savings

account that pays 7.2% annual interest, compounded annually. If you

make no other deposits into the account, how long will it take for the

account to grow to $3,000? Since this account has no regular payments

(PMT=0), the payment mode (End or Begin) is irrelevant.

3,000

_2,000

7. 2

* The PMT stored in the previous step is the 12-digit number −894.330557971.

The calculation of the balloon payment must use the actual monthly payment

amount: the rounded number $894.33, an exact dollars-and-cents amount.

72 5: Time Value of Money

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Keys: Display: Description:

" ] "Displays TVM menu.

@c #$ 5?@2 H<A 0EAH" Clears history stack and

TVM variables.

1 Y

#"5?@2 H<A"0EAH"

Sets one compounding

per./yr. (one interest

pmt./yr.). Payment mode

does not matter.

7.2 U ;6@28-&$(" Stores annual interest rate.

2000 & V 5O8/$K(((&((" Stores amount of deposit.

3000 X GO8%K(((&((" Stores future account

balance in FV.

T <8.&*%" Calculates number of

compounding periods

(years) for the account to

reach $3,000.

There is no conventional way to interpret results based on a non-integer

value (5.83) of N. Since the calculated value of N is between 5 and 6,

it will take 6 years of annual compounding to achieve a balance of at

least $3,000. The actual balance at the end of 6 years can be

calculated as follows:

6 T <8'&((" Stores a whole number of

years in N.

X GO8%K(%.&$*" Calculates account balance

after six years.

Example: An Individual Retirement Account (IRA). You opened an IRA

on April 15, 2003, with a deposit of $2,000. Thereafter, you deposit

$80.00 into the account at the end of each half-month. The account

pays 8.3% annual interest, compounded semimonthly. How much

money will the account contain on April 15, 2018?

5: Time Value of Money 73

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1 2 359 360

_80

_2,000

4/15/2018

4/15/2003

8.3

2 12; End mode

15 12 2

Keys: Display: Description:

" ] "Displays TVM menu. It is

not necessary to clear data

because you do not need to

set any of the values to

zero.

24 Y

[ e

$+ 5?@2 H<A 0EAH"

Sets 24 payment periods

per year. End mode.

15 @ T <8%'(&((" Figures and stores number

of deposits in N.

8.3 U ;6@28*&%(" Stores annual interest rate.

2000 & V 5O8/$K(((&((" Stores initial deposit.

80 & W 50:8/*(&((" Stores semimonthly

payment.

X GO8'%K,'%&*+" Calculates balance in IRA

after 15 years.

74 5: Time Value of Money

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Leasing Calculations

Two common leasing calculations are 1) finding the lease payment

necessary to achieve a specified yield, and 2) finding the present value

(capitalized value) of a lease. Leasing calculations typically use

“advance payments”. For the calculator, this means Begin mode

because all payments will be made at the beginning of the period. If

there are two payments in advance, then one payment must be

combined with the present value. For examples with two or more

advance payments, see pages 75 and 199.

Example: Calculating a Lease Payment. A new car valued at $13,500

is to be leased for 3 years. The lessee has the option to purchase the car

for $7,500 at the end of the leasing period. What monthly payments,

with one payment in advance, are necessary to yield the lessor 14%

annually? Calculate the payments from the lessor’s point of view. Use

Begin payment mode because the first payment is due at the inception

of the lease.

132343536

_13,500

7, 5 0 0

12; Be

in mode

Keys: Display: Description:

" ] "Displays TVM menu.

12 Y

Z e

#$ 5?@2 JH=;<"

0EAH"

Sets 12 payment periods

per year, Begin mode.

36 T <8%'&((" Stores number of payments.

5: Time Value of Money 75

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14 U ;6@28#+&((" Stores annual interest rate.

13500 &

5O8/#%K.((&(("

Stores car’s value in PV.

(Money paid out by lessor.)

7500 X GO8-K.((&((" Stores purchase option

value in FV. (Money

received by lessor.)

W 50:8$*,&#," Calculates monthly payment

received.

Example: Present Value of a Lease with Advance Payments and

Option to Buy. Your company is leasing a machine for 4 years.

Monthly payments are $2,400 with two payments in advance. You

have an option to buy the machine for $15,000 at the end of the

leasing period. What is the capitalized value of the lease? The interest

rate you pay to borrow funds is 18%, compounded monthly.

132 44 45464748

_15,000

－

4,800

_2,400

12; Be

in mode

The problem is done in four steps:

1. Calculate the present value of 47 monthly payments in Begin mode.

(Begin mode makes the first payment an advance payment.)

2. Add one additional payment to the calculated present value. This

adds a second advance payment to the beginning of the leasing

period, replacing what would have been the final (48th) payment.

3. Find the present value of the buy option.

4. Add the present values calculated in steps 2 and 3.

76 5: Time Value of Money

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Keys: Display: Description:

" ] "Displays TVM menu.

@c #$ 5?@2 H<A 0EAH" Clears history stack and

TVM variables.

12 Y

Z e

#$ 5?@2 JH=;<"

0EAH"

Sets 12 payment periods

per year; Begin mode.

Step 1: Find the present value of the monthly payments.

47 T <8+-&((" Stores number of payments.

18 U ;6@28#*&((" Stores annual interest rate.

2400 & W 50:8/$K+((&((" Stores monthly payment.

V 5O8*#K-%.&.*" Calculates present

(capitalized) value of the

47 monthly payments.

Step 2: Add the additional advance payment to PV. Store the answer.

+ 2400 = *+K#%.&.*" Calculates present value of

all payments.

s 0 *+K#%.&.*" Stores result in register 0.

Step 3: Find the present value of the buy option.

48 T <8+*&((" Stores number of payment

periods.

15000 &

GO8/#.K(((&(("

Stores amount of the buy

option (money paid out).

0 W 50:8(&((" There are no payments.

5: Time Value of Money 77

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V 5O8-K%+(&+%" Calculates present value

of the buy option.

Step 4: Add the results of step 2 and 3.

+R 0 = ,#K+-'&((" Calculates present,

capitalized value of lease.

Amortization (AMRT)

The AMRT menu (press ] . \ ) displays or prints the

following values:

! The loan balance after the payment(s) are made.

! The amount of the payment(s) applied toward interest.

! The amount of the payment(s) applied toward principal.

TVM

I%YR

INT

BEG

P/YR

PRIN

END

PMT

BAL

OTHER

TABLE

AMRT

78 5: Time Value of Money

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Table 5-2. AMRT Menu Labels

Label

Description

^ Stores the number of payments to be amortized, and

calculates an amortization schedule for that many

payments. Successive schedules start where the last

schedule left off. #P can be an integer from 1 through

1,200.

_ !

Displays the amount of the payments applied toward

interest.

` !

Displays the amount of the payments applied toward

principal.

a !

Displays the balance of the loan.

b !

Calculates the next amortization schedule, which

contains #P payments. The next set of payments starts

whe re the previous set left off.

c !

Displays a menu for printing an amortization table

(schedule).

Displaying an Amortization Schedule

For amortization calculations, you need to know PV, I%YR, and PMT. If

you have just finished doing these calculations with the TVM menu, then

skip to step 3.

To calculate and display an amortization schedule:*

1. Press " ] to display the TVM menu.

* Amortization calculations use values of PV, PMT, and INT rounded to the

number of decimal places specified by the current display setting. A setting of

+ 2 means that these calculations will be rounded to two decimal places.

5: Time Value of Money 79

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2. Store the values for I%YR , PV, and PMT. (Press & to make PMT a

negative number.) If you need to calculate one of these values, follow

the instructions under “Using the TVM Menu,” on page 66. Then go

on to step 3.

3. Press . to display the rest of the TVM menu.

4. If necessary, change the number of payment periods per year stored

in Y.

5. If necessary, change the payment mode by pressing JH= or H<A.

(Most loan calculations use End mode.)

6. Press \. (If you want to print the amortization schedule, go to

page 82 to continue.)

7. Key in the number of payments to be amortized at one time and press

^. For example, to see a year of monthly payments at one time,

set #P to 12. To amortize the entire life of a loan at one time, set #P

equal to the total number of payments (N).

If #P = 12, the display would show:

Current set of

ments to be amortized

Number of

ments

amortized at one time

Press to see results

8.To display the results, press, _ , ` and a (or press ]

to view the results from the stack).

9. To continue calculating the schedule for subsequent payments, do a

or b. To start the schedule over, do c.

a. To calculate the next successive amortization schedule, with the

same number of payments, press b.

80 5: Time Value of Money

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Next set of

ments authorized

successive

b. To calculate a subsequent schedule with a different number of

payments, key in that number and press ^.

c. To start over from payment #1 (using the same loan information),

press @c and proceed from step 7.

Example: Displaying an Amortization Schedule. To purchase your

new home, you have taken out a 30-year, $65,000 mortgage at 12.5%

annual interest. Your monthly payment is $693.72. Calculate the

amount of the first year’s and second year’s payments that are applied

toward principal and interest.

Then calculate the loan balance after 42 payments (3½ years).

Keys: Display: Description:

" ] "Displays TVM menu.

12.5 U ;6@28#$&.(" Stores annual interest

rate.

65000 V 5O8'.K(((&((" Stores loan amount.

693.72 &

50:8/',%&-$"

Stores monthly payment.

#$ 5?@2 H<A 0EAH"

If needed: sets 12

payment periods per

year; End mode.

\ 3H@ P50:FQ 52HFF"

RP5S"

Displays AMRT menu.

12 ^ P58#$ 50:FI #/#$" Calculates amortization

schedule for first 12

5: Time Value of Money 81

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payments, but does not

display it.

_ ;<:H2HF:8/*K##%&#'"Displays interest paid in

first year.

` 52;<7;5198/$##&+*" Displays principal paid in

first year.

a J191<7H8'+K-**&.$" Displays balance at end

of first year.

b P58#$ 50:FI #%/$+" Calculates amortization

schedule for next 12

payments.

_ ;<:H2HF:8/*K(*.&#."Displays results for

second year.

` 52;<7;5198/$%,&+,"

a J191<7H8'+K.+,&(%"

To calculate the balance after 42 payments (3½ years), amortize 18

additional payments (42－24＝18):

18 ^ P58#* 50:FI $./+$" Calculates amortization

schedule for next 18

months.

_ ;<:H2HF:8"

/#$K(''&,*"

Displays results.

` 52;<7;5198/+#,&,*"

a J191<7H8'+K#$,&(."

Printing an Amortization Table (TABLE)

To print an amortization schedule (or “table”) do steps 1 through 5 for

displaying an amortization schedule (see page 78).

82 5: Time Value of Money

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6. Press \ Ignore the message 3H@ P50:FQ 52HFF

RP5S.

7. Press c.

8. Key in the payment number of the first payment in the schedule and

press d. (For instance, for the very first payment, FIRST= 1.)

9. Key in the payment number of the last payment in the schedule and

press e.

10.Key in the increment ― the number of payments shown at one time―

and press f. (For instance, for one year of monthly payments at

a time, INCR=12.)

11.Press g.

Values are retained until you exit the TABLE menu, so you can print

successive amortization schedules by re-entering only those TABLE

values that change.

Example: Printing an Amortization Schedule. For the loan described

in the previous example (page 80), print an amortization table with

entries for the fifth and sixth years. You can continue from the AMRT

menu in the previous example (step 7, above) or repeat steps 1 through

Starting from the AMRT menu:

Keys: Display: Description:

c 52;<: 10E2:"

:1J9H"

Displays menu for

printing amortization

table.

4 * 12 + 1 d G;2F:8+,&((" The 49th is the first

payment in year 5.

6 * 12 e 91F:8-$&((" The 72nd is the last

payment in year 6.

12 f ;<728#$&((" Each table entry

represents 12 payments

5: Time Value of Money 83

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(1 year).

g "Calculates and prints

amortization schedule

shown below.

;6@28" #$&.("

5O8" '.K(((&(("

50:8" /',%&-$"

GO8" (&(("

5?@28" #$&(("

H<A 0EAH"

50:FI+,/'("

;<:H2HF:8" /-K,-'&*-"

52;<7;5198" /%+-&--"

J191<7H8" '%K'$$&,+"

50:FI'#/-$"

;<:H2HF:8" /-K,%(&*$"

52;<7;5198" /%,%&*$"

J191<7H8" '%K$$,&#$"

84 6: Interest Rate Conversions

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Interest Rate Conversions

The interest conversion (ICNV) menu converts between nominal and

effective interest rates. To compare investments with different

compounding periods, their nominal interest rates are converted to

effective interest rates. This allows you, for example, to compare a

savings account that pays interest quarterly with a bond that pays

interest semiannually.

! The nominal rate is the stated annual interest rate compounded

periodically, such as 18% per year compounded monthly.

! The effective rate is the rate that, compounded only once (that is,

annually), would produce the same final value as the nominal rate. A

nominal annual rate of 18% compounded monthly equals an effective

annual rate of 19.56%.

When the compounding period for a given nominal rate is one year,

then that nominal annual rate is the same as its effective annual rate.

6: Interest Rate Conversions 85

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The ICNV Menu

FIN

TVM

NOM% NOM%

PER

BUS

ICNV

EFF% EFF%

CONT

SUM

CFLO

TIME

BOND

SOLVE

DEPRC

CURRX

The ICNV menu converts between nominal and effective interest rates,

using either:

! Periodic compounding; for example, quarterly, monthly, or daily

compounding.

! Continuous compounding.

Converting Interest Rates

To convert between a nominal annual interest rate and an effective

annual interest rate that is compounded

periodically

1. Press " h to display the interest conversions menu.

2. Press i for periodic.

3. Key in the number of compounding periods per year and press

4. To convert to the effective rate, first key in the nominal rate and press

j, then press k.

5. To convert to the nominal rate, first key in the effective rate and press

k, then press j.

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To convert between a nominal annual interest rate and an effective

annual interest rate that is compounded

continuously

1. Press " h to get the interest conversions menu.

2. Press l for “continuous”.

3. To convert to the effective rate, key in the nominal rate and press

j, then press k.

4. To convert to the nominal rate, key in the effective rate and press

k, then press j.

Values of EFF% and NOM% are shared between the PER and CONT

menus. For example, an effective interest rate in CONT remains stored

in EFF% when you exit the CONT menu and enter the PER menu.

Pressing @c in either menu clears NOM% and EFF% in both.

NOM% NOM%

PER

ICNV

EFF% EFF%

CONT

Shared variables

between PER and CONT

Example: Converting from a Nominal to an Effective Interest Rate.

You are considering opening a savings account in one of three banks.

Which bank has the most favorable interest rate?

Bank #l 6.7% annual interest, compounded quarterly.

Bank #2 6.65% annual interest, compounded monthly.

Bank #3 6.65% annual interest, compounded continuously.

Keys: Display: Description:

" h "Displays ICNV menu.

i 7E05E4<A;<= 5"

:;0HF?@2"

Displays PER menu.

6: Interest Rate Conversions 87

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4 1 58+&((" Stores number of

compounding periods per

year for bank #1.

6.7 j <E068'&-(" Stores nominal annual

interest rate for bank #1.

k HGG68'&*-" Calculates effective

interest rate for bank #1.

12 1 58#$&((" Stores number of

compounding periods per

year for bank #2.

6.65 j <E068'&'." Stores nominal annual

interest rate for bank #2.

k HGG68'&*'" Calculates effective

interest rate for bank #2.

e l 7E<:;<4E4F"

7E05E4<A;<="

Displays CONT menu.

Previous values of NOM%

and EFF% are retained.

k HGG68'&**" Calculates effective rate

for bank #3.

The calculations show that bank #3 is offering the most favorable

interest rate.

Compounding Periods Different from

Payment Periods

The TVM menu assumes that the compounding periods and the payment

periods are the same. However, regularly occurring savings- account

deposits and withdrawals do not necessarily occur at the same time as

the bank’s compounding periods. If they are not the same, you can

adjust the interest rate using the ICNV menu, and then use the adjusted

88 6: Interest Rate Conversions

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interest rate in the TVM menu. (You can also use TVM if PMT = 0,

regardless of the compounding periods.)

1. Call up the periodic interest-rate conversion menu ( " h

i ).

2. Calculate the effective annual interest rate from the nominal annual

interest rate given by the bank.

a. Store annual interest rate in j.

b. Store number of compounding periods per year in 1.

c. Press k.

3. Calculate the nominal annual interest rate that corresponds to your

payment periods.

a. Store the number of regular payments or withdrawals you will be

making per year in 1.

b. Press

4. Return to the TVM menu (ee ] ).

5. Store the just-calculated nominal interest rate in I%YR (press s

U ).

6. Store the number of payments or withdrawals per year in Y and

set the appropriate payment mode.

7. Continue with the TVM calculation. (Remember that money paid out is

negative; money received is positive.)

a. N is the total number of periodic deposits or withdrawals.

b. PV is the initial deposit.

c. PMT is the amount of the regular, periodic deposit or withdrawal.

d. FV is the future value.

When the interest rate is the unknown variable, first calculate I%YR in

the TVM menu. This is the nominal annual rate that corresponds to your

payment periods. Next, use the ICNV menu to convert this to the

6: Interest Rate Conversions 89

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effective interest rate based on your payment periods. Last, convert the

effective rate to the nominal rate based on the bank’s compounding

periods.

Example: Balance of a Savings Account. Starting today, you make

monthly deposits of $25 into an account paying 5% interest

compounded daily (365-day basis). At the end of 7 years, how much

will you receive from the account?

Keys: Display: Description:

" h FH9H7:

7E05E4<A;<="

i 7E05E4<A;<= 5"

:;0HF?@2"

Periodic interest-rate

conversion menu.

365 1 58%'.&((" Stores bank’s

compounding periods.

5 j <E068.&((" Stores bank’s nominal

interest rate.

k HGG68.&#%"

Calculates effective interest

rate for daily compounding.

12 1 58#$&((" Stores number of deposits

per year.

j <E068.&(#" Calculates equivalent

nominal interest rate for

monthly compounding.

] <

.&(#"

Switches to TVM menu;

NOM% value is still in

calculator line.

s U ;6@28.&(#" Stores adjusted nominal

interest rate in I%YR.

. 12 Y

Z e

#$ 5?@2 JH=;< 0EAH"

Sets 12 payments per

year; Begin mode.

90 6: Interest Rate Conversions

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7 @ T

25& W

0 V

5O8(&(("

Stores 84 deposit periods,

$25 per deposit, and no

money before the first

regular deposit.

X GO8$K.#,&'#" Value of account in 7

years.

If the interest rate were the unknown, you would first do the TVM

calculation to get I%YR (5.01). Then, in the ICNV PER menu, store 5.01

as NOM% and 12 as P for monthly compounding. Calculate EFF%

(5.13). Then change P to 365 for daily compounding and calculate

NOM% (5.00). This is the bank’s rate.

7: Cash Flow Calculations 91

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Cash Flow Calculations

The cash flow (CFLO) menu stores and analyzes cash flows (money

received or paid out) of unequal (ungrouped) amounts that occur at

regular intervals.* Once you’ve entered the cash flows into a list, you

can calculate:

! The total amount of the cash flows.

! The internal rate of return (IRR%).

! The net present value (NPV), net uniform series (NUS), and net future

value (NFV) for a specified periodic interest rate (I%).

You can store many separate lists of cash flows. The maximum number

depends on the amount of available calculator memory.

The CFLO menu

FIN

TVM

CALC

TOTAL

BUS

ICNV

INSR

IRR%

SUM

CFLO

DELET

TIME

BOND

NAME

NPV

SOLVE

DEPRC

GET

NUS NFV

CURRX

The CFLO menu creates cash-flow lists and performs calculations with a

list of cash flows.

* You can also use CFLO with cash flows of equal amounts, but these are

usually handled more easily by the TVM menu.

92 7: Cash Flow Calculations

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Table 7-1. CFLO Menu Labels

Menu Label Description

E Accesses the CALC menu to calculate TOTAL, IRR%,

NPV, NUS, NFV.

m !

Allows you to insert cash flows into a list.

n !

Deletes cash flows from a list.

o !

Allows you to name a list.

p !

Allows you to switch from one list to another or

create a new list.

q !

Turns the prompting for #TIMES on and off.

To see the calculator line when this menu is in the display, press

I once. (This does not affect number entry.)

To see this menu when the calculator line is in the display, press e.

Cash Flow Diagrams and Signs of Numbers

The sign conventions used for cash flow calculations are the same as

those used in time-value-of-money calculations. A typical series of cash

flows is one of two types:

! Ungrouped cash flows. These occur in series of cash flows without

“groups” of equal, consecutive flows.* Because each flow is different

from the one before it, the number of times each flow occurs is one.

* Any cash flow series can be treated as an ungrouped one if you enter each

flow individually.

7: Cash Flow Calculations 93

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$200

$100

$300

$200

$ _ 50

$250

$125

Time

eriods

Mone

received is a

ositive number

Mone

aid out

is a ne

ative

number

12345678

Figure 7-1. Cash Flows (Ungrouped)

The horizontal timeline is divided into equal compounding periods. The

vertical lines represent the cash flows. For money received, the line

points up (positive); for money paid out, the line points down (negative).

In this case, the investor has invested $700. This investment has

generated a series of cash flows, starting at the end of the first period.

Notice that there is no cash flow (a cash flow of zero) for period five,

and that the investor pays a small amount in period six.

! Grouped cash flows. These occur in a series containing “groups” of

equal, consecutive flows. Consecutive, equal cash flows are called

grouped cash flows. The series shown here is grouped into two sets of

consecutive, equal cash flows:

94 7: Cash Flow Calculations

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123456789

$_100

$_200

Figure 7-2. Grouped Cash Flows

After an initial payment of $100, the investor pays $100 at the end of

periods 1 through 5, and $200 at the end of periods 6 through 8. The

investment returns $1,950 at the end of period 9. For every cash flow

you enter, the calculator prompts you to indicate how many times

(#TIMES) it occurs.

Creating a Cash-Flow List

To use CFLO, be sure your cash flows are occurring at regular intervals

and at the end of each period.* If a period is skipped, enter zero for its

cash flow. If there are any grouped (consecutive and equal) cash flows,

the #TIMES prompting makes entering the data easier.

* If the cash flows occur at the beginning of each period, then combine the first

flow with the initial flow (which can increase or decrease the flow), and move

each cash flow up one period. (Remember: a payment made at the beginning

of period 2 is equivalent to the same payment made at the end of period 1

and so on. Refer to pages 64-92.)

7: Cash Flow Calculations 95

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Entering Cash Flows

To enter cash flows into a CFLO list:

1. Press " r. You will see either G9ECL(T8U if the current

list is empty, or G9ECL# or moreT8U if the list is not empty. This is

the bottom of the current list.

2. If the list is not empty, you can do either a or b:

a. Clear the list by pressing @c W (see also page 99.)

b. Get a new list by pressing p s (The old list must be

named first. Press o or see page 97.)

3. If the cash flows are ungrouped (that is, they are all different), then

press q to turn P:;0HF 52E05:;<= EGG. For grouped cash

flows, leave this prompting on. (For more information, see “Prompting

for #TIMES,” next page.)

4. Key in the value of the initial cash flow, FLOW(0) (remember that

money paid out is negative ― use & to change the sign), and press

I.*

5. After briefly showing FLOW(0), the display shows G9ECL#T8U. (To

view FLOW(0) longer, hold down I before releasing it.) Key in

the value for FLOW(1) and press I. The prompt for the next

item appears.

6. For grouped cash flows: The display now shows

P:;0HFL#T8#. If it does not, press e q to turn the

#TIMES prompting on. (See “Prompting for #TIMES,” below.) #TIMES

is the number of consecutive occurrences of FLOW(1). #TIMES has

* You can do calculations with a number before entering it. This does not

interfere with the list. When you press I, the evaluated expression or

number is entered into the list.

96 7: Cash Flow Calculations

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been automatically set to 1, and #&(( is displayed on the calculator

line. Do either a or b:

a. To retain the value 1 and go on to the next flow, press I

(or ]).

b. To change #TIMES, key in the number and press I.*

Given #TIMES

Calculator line

7. Continue entering each cash flow and, for grouped flows, the number

of times it occurs. The calculator recognizes the end of the list when a

flow is left blank (no value is entered).

8. Press e to end the list and restore the CFLO menu. You can now

proceed to correct the list, name the list, get another list, or do

calculations with the values.

Use these same instructions to enter additional lists.

Prompting for #TIMES (#T?). When the calculator displays

P:;0HFL#T8#, it is prompting you for the number of times the current

flow occurs. If all your cash flows are different (#TIMES always 1), then

you don’t need the P:;0HF prompt. You can turn the prompting for

#TIMES on and off by pressing q in the CFLO menu. This

produces a brief message: either P:;0HF

52E05:;<=I EGG, or P:;0HF 52E05:;<=I E<.

While prompting is off, all cash flows you enter will have #TIMES = 1.

When you are viewing a cash-flow list with the #TIMES prompting off,

the calculator displays only those #TIMES values that are not 1.

* The maximum #TIMES for each cash flow is 999.

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The #TIMES prompting is usually on, because it is automatically turned

on whenever you clear or get a cash-flow list.

Example: Entering Cash Flows. Enter the following ungrouped cash

flows in a list and find the percentage internal rate of return (IRR).

0: $－500 2: $ 275

1: 125 3: 200

Keys: Display: Description:

" r "

@c 79H12 :MH 9;F:U" Asks for confirmation.

W G9ECL(T8U" Clears data from list and

prompts for initial flow.

q P:;0HF 52E05:;<=I"

EGG"

Sets prompting off be-

cause it is not needed.

500 &I G9ECL#T8U"

/.((&(("

Enters initial flow; then

immediately prompts for

next flow.

125 I G9ECL$T8U"

#$.&(("

Enters FLOW(1); prompts

for next flow.

275 I G9ECL%T8U"

$-.&(("

Enters FLOW(2); prompts

for next flow.

200 I G9ECL+T8U"

$((&(("

Enters FLOW(3); prompts

for next flow.

e E <5OK <4FK <GO <HHA"

;6"

Ends list and displays

CALC menu.

t ;2268,&('" Calculates IRR.

Viewing and Correcting the List

To display a particular list, use p (see page 99).

98 7: Cash Flow Calculations

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The [ and ] keys move up and down one number at a time.

@[ and @] display the beginning and end of the list.

Changing or Clearing a Number. To change a number after it’s been

entered: display the number, key in the new value, and press I.

Use this same method to clear a number to zero. (Do not press C or

<, which clear the calculator line, not the cash-flow entry.)

Inserting Cash Flows into a List. Insertion occurs before (above) the

current flow. Pressing m inserts a zero cash flow and renumbers

the rest of the list. You can then enter a new cash flow and its #TIMES.

For example, if FLOW(6) is in the display, pressing m puts a new,

zero flow between the previously numbered FLOW(5) and FLOW(6).

Deleting Cash Flows from a List. Pressing n deletes both the

current flow and its #TIMES.

Copying a Number from a List to the Calculator Line

To copy a number from the list into the calculator line, use ] or [ to

display the number, then press R I.

Naming and Renaming a Cash-Flow List

A new list has no name. You may name it before or after filling the list,

but you must name it in order to store another list.

To name a list:

1. Press o from the CFLO menu.

2. Use the ALPHA menu to type a name. (The ALPHA and ALPHA-Edit

menus are covered on pages 30 - 32.) To clear a name, press C.

3. Press I.

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The name can be up to 22 characters long and include any character

except:＋－ x ÷ ( ) < > : = space *

But only the first three to five characters (depending on letter widths) of

the name are used for a menu label. Avoid names with the same first

characters, since their menu labels will look alike.

Viewing the Name of the Current List. Press o, then e.

Starting or GETting Another List

When you press r, the cash-flow list that appears is the same as

the last one used.

To start a new list or switch to a different one, the current list must be

named or cleared. If it is named, then:

1. Press p.The GET menu contains a menu label for each named

list plus s.

2. Press the key for the desired list. ( s brings up a new, empty

list.)

Clearing a Cash-Flow List and Its Name

To clear a list’s numbers and name:

1. Display the list you want to clear, then press @c W. This

removes the numbers.

2. If the list is named, you’ll see 19FE 79H12 9;F: <10HU

Press W to remove the name. Press X to retain the name

with an empty list.

* CFLO does accept these exceptional characters in list names, but the Solver

functions SIZEC, FLOW, and #T do not.

100 7: Cash Flow Calculations

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To remove just one value at a time from a list, use n.

Cash-Flow Calculations: IRR, NPV, NUS, NFV

Once you have entered a list of cash flows, you can calculate the

following values in the CALC menu.

! Sum (TOTAL).

! Internal rate of return (IRR%). This is a periodic rate of return. To

calculate an annual nominal rate when the period is not a year,

multiply the IRR% by the number of periods per year.

If you want the IRR% as an effective annual rate, then use the FIN

ICNV menu to convert from the nominal annual rate to the effective

annual rate.

! Net present value (NPV), net uniform series (NUS), and net future

value (NFV) for a specified, periodic interest rate, I%.

7: Cash Flow Calculations 101

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Table 7-2. The CALC Menu for CFLO Lists

Menu Label Description

O Calculates the sum of the cash flows.

t* !

Calculates the internal rate of return―the interest

(discount) rate at which the net present value of the

cash flows equals zero.

u !

Stores the periodic interest rate, expressed as a

percentage (sometimes called cost of capital,

discount rate, or required rate of return).

v !

Given I%, calculates the net present value―the

present value of a series of cash flows.

w !

Given I%, calculates the net uniform series―the

dollar amount of constant, equal cash flows having

a present value equivalent to the net present value.

x !

Given I%, calculates the net future value of a series

of cash flows by finding the future value of the net

present value.

* The calculations for internal rate of return are complex and may take a

relatively long time. To interrupt the calculation, press any key. In certain

cases, the calculator displays a message indicating that the calculation

cannot continue without further information from you, or that there is no

solution. Refer to appendix B for additional information about calculating

IRR%.

About the Internal Rate of Return (IRR%). A “conventional investment”

is considered attractive if IRR% exceeds the cost of capital. A

conventional investment meets two criteria―(1) the sequence of cash

flows changes sign only once, and (2) the sum (TOTAL) of the cash flows

is positive.

Remember that the calculator determines a periodic IRR%. If the cash

flows occur monthly, then IRR% is a monthly value, too. Multiply it by 12

for an annual value.

102 7: Cash Flow Calculations

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Example: Calculating IRR and NPV of an Investment. An investor

makes an initial investment of $80,000, and expects returns over the

next five years as illustrated below.

$ _ 80,000

12345

5,000 4,500

5,500

4,000

115,000

(Initial flow)

Calculate the total of the cash flows and the internal rate of return of the

investment. In addition, calculate the net present value and net future

value, assuming an annual interest rate of 10.5%.

Start the problem with an empty cash-flow list. Since the cash flows are

ungrouped, each one occurs just once. Turn off the #TIMES prompt to

make cash-flow entry faster.

Keys: Display: Description:

"Displays current cash-flow

list and CFLO menu keys.

p s

G9ECL(T8U"

Clears current list or gets a

new one. The empty list

prompts for its initial cash

flow.

q P:;0HF 52E05:;<=I"

EGG"

Briefly shows the status of

q then returns to the

list. With prompting off,

all cash flows are

7: Cash Flow Calculations 103

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assumed to occur just

once.

80000 &

G9ECL#T8U"

/*(K(((&(("

Prompts for next cash

flow. Calculator line

shows last number

entered.

5000 I G9ECL$T8U" Stores $5,000 for

FLOW(1), prompts for

next flow.

4500 I G9ECL%T8U" Stores FLOW(2).

5500 I G9ECL+T8U" Stores FLOW(3).

4000 I G9ECL.T8U" Stores FLOW(4).

115000 I G9ECL'T8U" Stores final cash flow and

shows end of list.

e E

:E:198.+K(((&(("

Calculates sum of the cash

flows.

t ;2268##&,%" Calculates internal rate of

return.

10.5 u ;68#(&.(" Stores periodic interest

rate.

v <5O8+K--+&'%" Calculates NPV.

x <GO8-K*'.&,." Calculates NFV.

Now calculate the net present value at an interest rate of 10.5% if cash

flow #4 is reduced to $1,000.

e G9ECL'T8U" Displays the bottom of the

list.

[[ G9ECL+T8+K(((&((" Moves to cash flow #4.

1000 I G9ECL.T8##.K(((&(("Changes cash flow #4 to

$1,000.

104 7: Cash Flow Calculations

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e E

<5O8$K-'$&+%" Calculates new NPV.

Example: An Investment with Grouped Cash Flows. You are

considering an investment that requires a cash outlay of $9,000, with

the promise of monthly cash flows as shown. Calculate IRR%. Also find

NPV and NFV at an annual interest rate of 9%.

$ _ 9,000

500

1,000

1,500

Since some of these cash flows are grouped (consecutive and equal),

the #TIMES prompting must be on so you can specify a number other

than 1.

Group Number Amount Number of Times

Initial

－9,000

500

1,000

1,500

－

Keys: Display: Description:

"Current cash-flow list and

CFLO menu.

G9ECL(T8U"

Clears current list. #TIMES

prompting is turned on.

7: Cash Flow Calculations 105

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9000 & I G9ECL#T8U" Stores the initial cash

flow.

500 I P:;0HFL#T8#" Stores FLOW(1) and

prompts for #TIMES(1).

3 I G9ECL$T8U" FLOW(1) occurs 3 times;

prompts for next cash

flow.

1000 I 4

G9ECL%T8U"

Stores FLOW(2) four

times.

0 I

G9ECL+T8U"

Stores FLOW(3) one time

(the 1 is automatically

entered).

1500 I 3

G9ECL.T8U"

Stores FLOW(4) three

times.

e E "Displays the CALC menu.

t ;2268#&.%" Calculates monthly IRR%.

9 / 12

;68(&-."

Stores the periodic,

monthly interest rate.

v <5O8+,$&,." Calculates NPV.

x <GO8.%.&#*" Calculates NFV.

Example: An Investment with Quarterly Cash Returns. You have been

offered an opportunity to invest $20,000. The investment returns

quarterly payments over four years as follows:

Year 1 4 payments of $500

Year 2 4 payments of $1,000

Year 3 4 payments of $2,000

Year 4 4 payments of $3,000

106 7: Cash Flow Calculations

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500

1,000

2,000

3,000

Calculate the annual rate of return for this investment. (The prompting for

#TIMES should be on.)

Keys: Display: Description:

" r "Current cash-flow list.

p s

G9ECL(T8U"

Clears the current list or

gets a new one. This sets

the #TIMES prompting on.

20000 &

G9ECL#T8U"

Stores the initial cash

flow.

500 I P:;0HFL#T8#" Stores FLOW(1), then

prompts for number of

times this flow occurs.

4 I G9ECL$T8U" FLOW(1) occurs four

times.

1000 I 4

2000 I 4

3000 I 4

Stores FLOW(2), FLOW(3)

and FLOW(4), and the

number of times each flow

occurs.

7: Cash Flow Calculations 107

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I G9ECL.T8U"

e E

;2268$&+%"

Calculates quarterly rate

of return.

* 4 = ,&-$" Calculates nominal annual

rate of return from

quarterly rate.

Doing Other Calculations with CFLO Data

If you would like to do other calculations with cash flows besides those

in the CALC menu, you can do so by writing your own Solver equations.

There are Solver functions that can access data stored in CFLO lists, and

there is a summation function that can combine all or part of the values

stored in specific lists.

Refer to “Accessing CFLO and SUM Lists from the Solver” in chapter 12.

108 8: Bonds

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Bonds

The BOND menu calculates the yield to maturity or price of a bond. It

also calculates yield to call on a coupon date and accrued interest. You

can specify the:

! Calendar basis: 30/360 or actual/actual (days per month/days per

year). Municipal, state, and corporate bonds issued in the United

States are typically 30/360. U.S. Treasury bonds are actual/actual.

! Coupon payments: semi-annual or annual. Most U.S. bonds are

semi-annual.

The BOND Menu

FIN

TVM

TYPE

YLD%

BUS

ICNV

SETT

PRICE

SUM

CFLO

MAT

ACCRU

TIME

BOND

CPN%

SOLVE

DEPRC

CALL MORE

CURRX

Pressing y shows you the BOND menu and the type of bond

currently specified: %(?%'( or 1?1; FH0;1<<419 or 1<<419.

8: Bonds 109

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Table 8-1. BOND Menu Labels

Label

Description

z Displays a menu of bond types: 30/360 or

actual/actual, semi-annual or annual.

{ !

Stores the settlement (purchase) date according to the

current date format (MM.DDYYYY or DD.MMYYYY;

see page 143).

| !

Stores the maturity date or call date according to the

current date format. The call date must coincide with

a coupon date.

} !

Stores the annual coupon rate as a percentage.

Stores the call price per $100 face value. For a yield

to maturity, make sure CALL equals 100. (A bond at

maturity has a “call” value that is 100% of its face

value.)

~ !

)

• !

Stores or calculates the yield (as an annual

percentage) to maturity or yield to call date.

* !

Stores or calculates the price per $100 face value.

€ !

Calculates the interest accrued from the last

coupon-payment date until the settlement date, per

$100 face value.

The calculator retains the values of the BOND variables until you clear

them by pressing @c while the BOND menu is displayed.

Clearing sets CALL to 100 and all other variables to zero.

To see the value currently stored in a variable, press R menu label.

110 8: Bonds

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Doing Bond Calculations

Remember that values in the BOND menu are expressed per $100 face

value or as a percentage. A CALL value of 102 means that the bond will

be worth $102 for every $100 of face value when called. Some

corporate bonds in the United States use the convention that the price of

the bond is set to 100 if the coupon rate equals the yield, whether or not

the settlement date is a coupon date. The BOND menu does not use this

convention.

To calculate the price or yield of a bond:

1. Display the BOND menu: press " y.

2. Press @c. This sets CALL=100.

3. Define the type of bond. If the message in the display does not match

the type you want, press z.

Calendar basis Interest period

! Pressing

• sets the calendar basis to a 30-day month and a

360-day year.

! Pressing

‚ sets the calendar basis to the actual calendar

month and to the actual calendar year.

! Pressing

ƒ sets semi-annual coupon payments.

! Pressing

„ sets annual coupon payments.

Press e to restore the BOND menu.

4. Key in the settlement date (MM.DDYYYY or DD.MMYYYY depending

on the date format; see chapter 11) and press {.

5. Key in the maturity date or call date and press |.

6. Key in the coupon rate as an annual percent and press }.

7. Key in the call value, if any, and press ~. For a bond held to

8: Bonds 111

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maturity, the CALL value must equal 100. (See step 3.)

8. To calculate a result, first press ) to access the remaining menu

labels. Do either a or b:

a. Key in the yield and press •. Press * to calculate the

price.

b. Key in the price and press *. Press • to calculate the

yield.

To calculate the accrued interest, press €. The total amount owed

the seller is PRICE + ACCRU, that is: * + € =.

Calculating Fractional Values. When given a fractional value that must

be entered in decimal form, do the arithmetic and then store the result

directly into a variable. Do not clear the arithmetic and then retype the

result before storing it―this is an unnecessary step that can cause

incorrect answers due to rounding. See how the following example

stores 83/8 in YLD%.

Example: Price and Yield of a Bond. What price should you pay on

August 10, 2003 for a 6¾% U.S. Treasury bond that matures on May 1,

2018 if you wish a yield of 83/8%? The calendar basis is actual/actual

and the coupon payments are semi-annual. (The example assumes

MM.DDYYYY date format.)

Keys: Display: Description:

" y

"Since there is no call on

this bond, set CALL = 100

by clearing variables.

z ‚

ƒ e

1?1 FH0;1<<419"

Sets bond type, if

necessary.

8.102003

{

FH::8"

(*?#(?$((% F4<"

Stores settlement

(purchase) date.

5.012018 "Stores maturity date.

112 8: Bonds

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

| 01:8(.?(#?$(#*

:4H"

6.75 } 75<68'&-." Stores annual coupon

rate.

)

3 / 8 + 8

•

@9A68*&%*"

Stores desired yield

(displayed rounded to two

decimal places).*

* 52;7H8*'&%*" Result: price is $86.38

per $100 face value.

+ € *'&%*)#&*." Adds accrued interest

owed the seller.

= **&$%" Net price.

Suppose that the market quote for the bond is 88¼. What yield does it

represent?

88.25 * 52;7H8**&$." Stores quoted price.

• @9A68*&#%" Result: yield to maturity.

Example: A Bond with a Call Feature. What is the price of a 6%

corporate bond maturing on March 3, 2022 and purchased on May 2,

2003 to yield 5.7%? It is callable on March 3, 2006 (a coupon date),

at a value of 102.75. What is the yield to the call date? Use a 30/360

calendar with semi-annual coupon payments.

Keys: Display: Description:

" y

"Displays BOND menu,

clears variables.

z •

ƒ e

%(?%'( FH0;1<<419"

Sets bond type, if

necessary.

* To see the full precision of the number, press @S.

8: Bonds 113

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5.022003 { FH::8"

(.?($?$((% G2;"

Stores purchase date

(MM.DDYYYY format).

3.032022 | 01:8(%?(%?$($$ :M4" Stores maturity date.

6 } 75<68'&((" Stores annual coupon

rate.

)

5.7 •

@9A68.&-("

Stores yield.

* 52;7H8#(%&+%" Calculates price.

) 3.032006

| 102.75

71998#($&-."

Changes maturity date

to call date and stores

a call value.

) • @9A68.&.*" Calculates yield to call.

Example: A Zero-Coupon Bond. Calculate the price of a zero-coupon,

semi-annual bond using a 30/360 calendar basis. The bond was

purchased on May 19, 2003 and will mature on June 30, 2017, and

has a yield to maturity of 10%.

Keys: Display: Description:

" y

"Clears BOND

variables, setting CALL

to 100.

z •

ƒ e

%(?%'( FH0;1<<419"

Sets type if necessary

(check the display).

5.192003

{

FH::8"

(.?#,?$((% 0E<"

Purchase date

(MM.DDYYYY format).

6.302017

01:8('?%(?$(#- G2;"

Maturity date.

0 } 75<68(&((" Coupon rate is zero.

) 10 • @9A68#(&((" Yield to maturity.

* 52;7H8$.&$%" Calculates price.

114 9: Depreciation

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Depreciation

The DEPRC (depreciation) menu calculates depreciation values and

remaining depreciable values one year at a time. The methods available

are:

! Declining balance.

! Sum-of-the-years’ digits.

! Straight line.

! Accelerated Cost Recovery System.

The DEPRC Menu

FIN

TVM

BASIS

YR#

BUS

ICNV

SALV

FACT%

SUM

CFLO

LIFE

DB SOYD SL

TIME

BOND

ACRS%

SOLVE

DEPRC

ACRS MORE

CURRX

Pressing … displays the DEPRC menu.

9: Depreciation 115

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Table 9-1. DEPRC Menu Labels

Label

Description

† Stores the depreciable cost basis of the asset at

acquisition.

‡ !

Stores the salvage value of the asset at the end of its

useful life. If there is no salvage value, set SALV=0.

ˆ !

Stores the expected useful life (in whole years) of the

asset.

‰ !

Stores the appropriate Accelerated Cost Recovery

System percentage from the published ACRS tables.

Calculates the ACRS deduction based on BASIS and

ACRS%. (The values in SALV, LIFE, FACT%, and YR#

do not matter.)

Š !

)

‹ !

Stores the number of the year for which you want the

depreciation (1, 2, etc.).

Œ !

Stores the declining-balance factor as a percentage

of the straight-line rate. This is for the DB method only.

For example, for a rate 1¼ times (125%) the

straight-line rate, enter 125.

• !

Calculates the declining-balance depreciation for the

year.

Ž !

Calculates the sum-of-the-years‘-digits depreciation for

the year.

• !

Calculates the straight-line depreciation for the year.

]!Displays the remaining depreciable value, RDV, after

you have pressed •, Ž, or •.

The calculator retains the values of the DEPRC variables until you clear

them by pressing @c while the DEPRC menu is displayed.

116 9: Depreciation

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To see the value currently stored in a variable, press R menu label.

Doing Depreciation Calculations

DB, SOYD, and SL Methods

To calculate the depreciation for an asset:*

1. Display the DEPRC menu: press " ….

2. Define the characteristics of the asset:

a. Key in the cost basis and press †

b. Key in the salvage value and press ‡. If there is no salvage

value, enter zero.

c. Key in the useful life and press ˆ.

3. Press ) for the rest of the DEPRC menu.

4. Key in the number for the year of depreciation you want to calculate

(1, 2, 3, etc.) and press ‹.

5. If you are using the declining-balance method, enter the DB factor (a

percentage) and press Œ.

6. Press •, Ž, or • to calculate the appropriate

depreciation.

7. To see the remaining depreciable value (basis ― salvage value ―

accumulated depreciation), press ].

8. To calculate the depreciation for another year, just change YR# and

press •, Ž, or • again.

* The calculated values of RDV, DB, SOYD, and SL are rounded internally to the

number of decimal places specified by the current display setting. A setting of

+ 2 means that these values will be rounded internally to two decimal

places.

9: Depreciation 117

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Example: Declining-Balance Depreciation. A metalworking machine,

purchased for $10,000, is to be depreciated over 5 years. Its salvage

value is estimated at $500. Find the depreciation and remaining

depreciable value for each of the first 3 years of the machine’s life using

the double-declining-balance method (200% of the straight-line rate). For

comparison, find the straight-line depreciation, as well.

Keys: Display: Description:

" … "Displays DEPRC menu.

10000 † J1F;F8#(K(((&((" Cost basis.

500 ‡ F19O8.((&((" Salvage value.

5 ˆ 9;GH8.&((" Useful life.

) 1 ‹ @2P8#&((" First year of depreciation.

200 Œ G17:68$((&((" DB percentage factor.

• AJ8+K(((&((" Depreciation in first year.

(Salvage value ignored at

this point.)

] 2AO8.K.((&((" Remaining depreciable

value after first year

(BASIS - SALV - 4,000).

2 ‹ • AJ8$K+((&((" Depreciation in second

year.

] 2AO8%K#((&((" Remaining depreciable

value after second year.

3 ‹ • AJ8#K++(&((" Depreciation in third year.

] 2AO8#K''(&((" Remaining depreciable

value after third year.

• F98#K,((&((" Straight-line depreciation

for each year.

118 9: Depreciation

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

] 2AO8%K*((&((" Remaining depreciable

value after third year

using SL.

The ACRS Method

To calculate the amount of tax deduction under the U.S. Accelerated

Cost Recovery System:

1. Display the DEPRC menu: press " ….

2. Enter the cost basis of the asset and press †

3. The Internal Revenue Service publishes tables that list the percentage

of an asset’s basis that can be deducted each year of its prescribed

life. Look up that value, enter it, and press ‰.

4. Press Š to calculate the value of the deduction.

Example: ACRS Deductions. Use the ACRS method to find the in-

come-tax deduction for a $25,000 asset over 3 years of a 5-year life.

Use this hypothetical ACRS table:

Year Percentage Deductible

Keys: Display: Description:

" … "DEPRC menu.

25000 † J1F;F8$.K(((&((" Enters basis.

15 ‰ 172F68#.&((" Tabular value, year 1.

Š 172F8%K-.(&((" Deduction in first year.

9: Depreciation 119

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25 ‰ 172F68$.&((" Tabular value, year 2.

Š 172F8'K$.(&((" Deduction in second year.

20 ‰ 172F68$(&((" Tabular value, year 3.

Š 172F8.K(((&((" Deduction in third year.

Partial-Year Depreciation

When the acquisition date of an asset does not coincide with the start of

the tax or fiscal year, then the amounts of depreciation in the first and

last years are computed as fractions of a full year’s depreciation. Except

in SL, the intermediate years are computed as sums of fractions. This

does not apply to the ACRS method.

Suppose you acquired an asset in October and wanted to depreciate it

for 3 years. (Your fiscal year begins January 1st.) The depreciation

schedule would affect parts of 4 years, as shown in the illustration. The

3 months from October to December equal ¼ year.

Number of months

Calendar

years

Depreciation

years

3-year life

For SL depreciation, partial-year calculations are easy: calculate the SL

value, then use ¼ of that value for the first year, the full amount the

second and third years, and ¾ of that amount the fourth year.

For DB and SOYD depreciation, each year’s depreciation value is

different, as shown in the table:

120 9: Depreciation

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

Calendar Year Depreciation Value

1 (Oct.-Dec.)

4 (Jan.-Sept.)

¼ x year 1

(¾ x year 1) + (¼ x year 2)

(¾ x year 2) + (¼ x year 3)

¾ x year 3

Example: Partial-Year Depreciation. A movie camera bought for

$12,000 has a useful life of 10 years with a salvage value of $500.

Using the sum-of-the-years’-digits method, find the amount of

depreciation for the fourth year. Assume the first depreciation year was

11 months long.

Keys: Display: Description:

" … "Displays DEPRC menu.

12000 †

500 ‡

10 ˆ

) 3 ‹

@2P8%&(("

Stores known values.

Ž FE@A8#K'-$&-$" Calculates depreciation

for year 3.

/ 12= s 1 #%,&%," Stores 1 month’s

depreciation from year 3.

4 ‹ Ž FE@A8#K+'%&'+" Calculates depreciation

for year 4.

* 11/ 12 = #K%+#&'-" Figures 11 months’

depreciation from year 4.

+R 1 = #K+*#&('" Figures total depreciation

for year 4.

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Running Total and Statistics

The SUM menu stores and statistically analyzes sets of numbers. As you

enter the numbers, the calculator displays their running total. Once

you’ve entered the numbers into a list, you can:

! Calculate the mean, median, standard deviation, and range.

! Display the largest and smallest number in the list.

! Sort the list from smallest number to largest number.

With two lists of numbers, you can:

! Do curve-fitting and forecasting calculations using two SUM lists and

one of four models―linear, exponential, logarithmic, and power.

(Curve fitting for the linear model is called linear regression.)

! Calculate the weighted mean and grouped standard deviation.

! Find the summation statistics (∑x, ∑x2, ∑y, ∑y2, ∑xy).

You can store many separate lists of numbers in SUM. The maximum

number depends on the amount of available calculator memory.

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The SUM Menu

FIN

CALC

TOTAL

MIN

BUS

INSR

MEAN

MAX

SUM

DELET

MEDN

SORT FRCST

TIME

NAME

STDEV

SOLVE

GET TOTAL

RANGE MORE

…

CURRX

The SUM menu creates lists of numbers and performs calculations with a

SUM list.

Table 10-1. SUM Menu Labels

Label

Description

E Accesses the CALC menu to calculate the total, mean,

median, standard deviation, range, minimum,

maximum, sorting, and linear regression (including

weighted mean and summation statistics).

m !

Allows you to insert numbers into the list.

n !

Deletes numbers from the list.

o !

Allows you to name the list.

p !

Allows you to switch from one named list to another

or to create a new list.

O !

Displays the total of all the items in the list.

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To see the calculator line when this menu is in the display, press

I once. (This does not affect number entry.)

To see this menu when the calculator line is in the display, press e.

Creating a SUM List

To keep a running total of a list of numbers or do statistical calculations

with sets of data, first create a SUM list of the values.

Entering Numbers and Viewing the TOTAL

To enter numbers into a SUM list:

1. Press $. You’ll see ;:H0L#T8U if the current list is empty, or

;:H0L2 or moreT8U if the list is not empty. This is the bottom of the

current list.

2. If the list is empty, start filling it (step 3). If the current list is not empty,

you can do either a or b:

a. Clear the list by pressing @c W (see also page

127.)

b. Get a new list by pressing p s (The old list must be

named first. Press o or see page 126.)

3. Key in the value of the first item, ITEM(1) (press & for a negative

number), and press I.* (To view ITEM(1) longer, hold down

I before releasing it.)

* Remember that you can do calculations with a number before entering it. This

does not interfere with the list. Whenever you press I, the number (or

evaluated expression) in the calculator line is entered into the list. If you need

to use the MATH menu, just press @m, do the calculation, then press e)

to return to where you were in SUM.

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After briefly showing ITEM(1), the display shows

" ;:H0L$T8U"

:E:19=number

TOTAL is the updated, running TOTAL of all the numbers in the list

(only one number, so far).

4. To enter ITEM(2), key in the value and press I. The prompt for

ITEM(3) and the new, updated total appear.

5. Continue entering values for ITEM(3), ITEM(4), etc. The calculator

recognizes the end of the list when an item is left blank (no value is

entered).

6. Press e to end the list and restore the SUM menu. You can now

proceed to correct the list, name the list, get another list, or do

statistical calculations.

Use these same instructions to enter additional lists.

Viewing and Correcting the List

To display a particular list, use p (see page 127).

The [ and ] keys move up and down the list one number at a time.

@[ and @] display the beginning and end of the list.

Changing or Clearing a Number. To change a number after it’s been

entered: display the number, key in the new value, and press I.

Use the same method to clear a number to zero. (Do not press C or

<, which clears the calculator line.)

Inserting Numbers into a List. Insertion occurs before (or above) the

current entry. Pressing m inserts a zero item and renumbers the rest

of the list. You can then enter a new value.

For example, if ITEM(6) is in the display, pressing m puts a new,

zero item between the previously numbered ITEM(5) and ITEM(6).

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Deleting Numbers from a List. Pressing n deletes the current item.

Example: Updating a Checkbook. On May 31, your checking account

balance was $267.82. The transactions for the first 10 days in June

are:

Date Transaction Amount Date Transaction Amount

6/1 Balance 267.82 6/3 Check －128.90

6/1 Deposit 837.42 6/7 Check － 65.35

6/1 Check －368.23 6/10 Deposit 55.67

6/2 Check －45.36

Update the checkbook by calculating the running balance.

Keys: Display: Description:

$ * "

@cW

;:H0L#T8U" Displays empty SUM list.

267.82 I ;:H0L$T8U"

:E:198$'-&*$"

Enters beginning balance

and shows running total.

837.42 I ;:H0L%T8U"

:E:198#K#(.&$+"

Enters deposit on 6/1.

368.23 &

45.36 &

128.90 &

65.35 &

Enters remaining

transactions.

* If you want to preserve the current list, skip the next step (pressing @c).

Instead, name the list and then press p s.

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55.67 I ;:H0L*T8U"

:E:198..%&(-"

e ;:H0L*T8U" Ends list and displays

SUM menu again.

Copying a Number from a List to the Calculator Line

To copy a number from the list into the calculator line, use ] or [ to

display the number, then press R I.

Naming and Renaming a SUM List

A new list has no name. You may name it before or after filling the list,

but you must name it in order to store another list.

To name a list:

1. Press o from the SUM menu.

2. Use the ALPHA menu to type in a name. (The ALPHA and ALPHA-Edit

menus are covered on pages 30 - 32.) To clear a name, press C.

3. Press I.

The name can be up to 22 characters long and include any character

except: ＋－ x ÷ ( ) < > : = space *

But only the first three to five characters (depending on letter widths) of

the name are used for a menu label. Avoid names with the same first

characters, since their menu labels will look alike.

Viewing the Name of the Current List. Press o, then e.

* SUM does accept these exceptional characters in list names, but the Solver

functions SIZES and ITEM do not.

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Starting or GETting Another List

When you press $, the SUM list that appears is the last one used.

To start a new list or switch to a different one, the current list must be

named or cleared. If it is named, then:

1. Press p. The GET menu contains a menu label for each named

list plus s.

2. Press the key for the desired list. ( s brings up a new, empty list.)

Clearing a SUM List and Its Name

To clear a list’s numbers and name:

1. Display the list you want to clear, then press @c W. This

removes the numbers.

2. If the list is named, you’ll see 19FE 79H12 9;F: <10HU Press

W to remove the name. Press X to retain the name with an

empty list.

To remove just one value at a time from a list, use n.

Doing Statistical Calculations (CALC)

Once you have entered a list of numbers, you can calculate the

following values.

! For one variable: the total, mean, median, standard deviation, range,

minimum, and maximum. You can also sort the numbers in order of

increasing value.

! For two variables: x-estimates and y-estimates (this is also called

forecasting), the correlation coefficient for different types of curves

(this is curve-fitting), the slope and y-intercept of the line, and

summation statistics. You can also find the weighted mean and the

grouped standard deviation.

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Calculations with One Variable

The CALC menu calculates the following statistical values using one

SUM list.

Table 10-2. The CALC Menu for SUM Lists

Menu Key Description

O !

Calculates the sum of the numbers in the list.

• !

Calculates the arithmetic mean (average).

‘ !

Calculates the median.

’ !

Calculates the standard deviation.*

Calculates the difference between the largest and

smallest number.

“ !

)

” !

Finds the smallest (minimum) number in the list.

• !

Finds the largest (maximum) number in the list.

– Sorts the list in ascending order.

— Displays a series of menus for calculations with two

variables for curve fitting, estimation, weighted mean

and grouped standard deviation, and summation

statistics.

* The calculator finds the sample standard deviation. The formula assumes

that the list of numbers is a sampling of a larger, complete set of data. If the

list is, in fact, the entire set of data, the true population standard deviation

can be computed by calculating the mean of the original list, placing that

value into the list, and then calculating the standard deviation.

Example: Mean, Median, and Standard Deviation. Suppose your

shop had the following phone bills during the past six months:

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Month Phone

Expense Month Phone

Expense

1. May

2. June

3. July

$340

$175

$450

4. August

5.September

6. October

$780

$245

$625

Calculate the mean, median, and standard deviation of the monthly

phone bills. Then display the smallest value in the list.

Keys: Display: Description:

$ Displays current SUM list

and SUM menu keys.

p s

;:H0L#T8U"

Clears current list or gets a

new one.

340 I ;:H0L$T8U"

:E:198%+(&(("

Stores May’s phone bill;

shows total.

175 I ;:H0L%T8U"

:E:198.#.&(("

Stores June; updates total.

450 I

780 I

245 I

625 I

;:H0L-T8U"

:E:198$K'#.&(("

Stores phone bills for

July-October and keeps a

running total.

e E $K'#.&((" Displays CALC menu.

• 0H1<8+%.&*%" Calculates mean.

‘ 0HA;1<8%,.&((" Calculates median.

’ #F:AHO8$%#&.." Calculates standard

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deviation.

) "Displays rest of CALC

menu.

” 0;<8#-.&((" Finds smallest number.

Calculations with Two Variables (FRCST)

The FRCST menu does the following two-variable calculations using two

SUM lists:

! Fits x- and y-data to a linear, logarithmic, exponential, or power

curve.

! Forecasts estimated values based on that curve.

! Finds the weighted mean and grouped standard deviation.

! Shows you the summation statistics (Σx, Σx2, Σy, Σy2, Σxy, etc.).

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CALC

TOTAL

x-list

X X2 Y2 XY Y

MODL

MIN

MEAN

-list

W.MN

MAX

MEDN

CORR

G.SD

SORT FRCST

(select x and

)

STDEV

RANGE

SIZE

LIN LOG EXP PWR

After pressing —, you must specify two previously created lists―

one for the x-variable and one for the y-variable. The two lists must have

the same number of items.

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Table 10-3. FRCST Menu Labels

Menu Label Description

list name for x-variable

list name for y-variable

These specify the two lists of data to be

compared. Also used for estimations:store

x and estimate y, or vice-versa. ˜ is

the menu label for an unnamed current list.

™* Calculates the correlation coefficient, a

number between －1 and ＋1 that

measures how closely the x,y data points

match the calculated curve.

š* Calculates M. For the linear model, this is

the slope.

Calculates B. For the linear model, this is

the y-intercept.

›*

)

œ Displays a choice of the four curve-fitting

models:

•, H, I, and ž.

Ÿ !Calculates the weighted mean of the

x-values using the weights in the y-list.

!Calculates the standard deviation of a set

of x-values grouped by frequencies

specified in the y-list.

The number of items in either list.

¡ !

)

¢ !Sum of items in x-list.

£ !Sum of items in y-list.

¤ !Sum of squares of items in x-list.

¥ !Sum of squares of items in y-list.

¦ !Sum of products of items in x- and y-lists.

* For the non-linear models, the calculation uses the transformed data values.

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Curve Fitting and Forecasting

Curve fitting is a statistical method for finding a relationship between

two variables, x and y. Based on this relationship, you can estimate new

values of y based on a given x-value, and vice-versa. Each SUM list

holds the numbers (data values) for one variable. You can select one of

four curve-fitting models:*

Linear Curve Fit

arithmic Curve Fit

onential Curve Fit

Power Curve Fit

* The exponential, logarithmic, and power models are calculated using

transformations that allow the data to be fitted by standard linear regression.

The equations for these transformations appear in appendix B. The

logarithmic model requires positive x-values; the exponential model requires

positive y-values; and the power curve requires positive x- and y-values.

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To do curve fitting and forecasting :

1. Enter the data into two SUM lists: one for the x-values and one for the

y-values. Make sure each list has the same number of items so that the

items are in matched pairs.

2. From the SUM menu, press E ) — to display a menu

of SUM-list names. The current list is labeled ˜ unless named

otherwise.

3. Press a menu key to select a list of x-values (independent variable).

4. Select a list of y-values (dependent variable).

5. Now you see the FRCST menu. Whichever curve-fitting model was

used last is named in the display. If you want to select a different

model, press ) œ, and then the menu key for the model.

6. To calculate the curve-fitting results, press, ™, š and

›.

7. To forecast (estimate) a value:

a. Key in the known value and press the menu key for that variable.

b. Press the menu key for the variable whose value you want to

forecast.

Example: Curve Fitting. BJ’s Dahlia Garden advertises on a local radio

station. For the past six weeks, the manager has kept records of the

number of minutes of advertising that were purchased, and the sales for

that week.

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Number of Minutes

of Radio

Advertising

(x-values,

MINUTES

)

Dollar Sales

(y-values,

SALES

)

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

$1,400

$ 920

$1,100

$2,265

$2,890

$2,200

BJ’s wants to determine whether there is a linear relationship between

the amount of radio advertising and the weekly sales. If a strong

relationship exists, BJ’s wants to use the relationship to forecast sales. A

graph of the data looks like this:

01234567 x

1,000

2,000

3,000

SALES in Dollars

of Advertisin

(forecasted)

M425.88

＝

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Keys: Display: Description:

$ "Displays current SUM list

and SUM menu keys.

;:H0L#T8U"

Clears current list.

2 I

1 I

3 I

5 I

4 I

;:H0L-T8U"

:E:198$(&(("

Stores minutes of

advertising (x-values) into

a SUM list.

e o :@5H"1"<10HIV;<54:W"

MINUTES

;:H0L-T8U"

Names this list. (See page

30 to use the ALPHA

menu.)

Now enter and name the second list.

p s ;:H0L#T8U" Gets a new, empty list.

1400 I

920 I

1100 I

2265 I

2890 I

2200 I

;:H0L-T8U"

:E:198#(K--.&(("

Stores weekly sales

(y-values) into a second

SUM list.

e o :@5H"1"<10HIV;<54:W"

SALES I ;:H0L-T8U" Names y-list.

E )

—

FH9H7: X O12;1J9H"

Identifies the lists for

curve-fitting.

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0;<4"

F19HF"

FH9H7: @ O12;1J9H"

9;<H12 *"

Selects MINUTES as x-list,

SALES as y-list, indicates

current curve-fitting

model, and displays

FRCST menu.

™ 7E228(&,(" Correlation coefficient for

linear model.

The correlation coefficient calculated above is acceptable to BJ’s. Using

the linear model, estimate what the level of sales would be if the

business purchased 7 minutes of advertising time per week.

7 "

0;<4" 0;<4:HF8-&((" Stores 7 in variable

MINUTES.

F19HF" F19HF8%K%.-&%*" Forecasts the sales

resulting from 7 minutes of

radio advertising.

How many minutes of advertising should BJ’s buy if it wants to attain

sales of $3,000?

3000 "

F19HF"

0;<4"

0;<4:HF8'&#'"

The business should buy

about 6 minutes of

advertising for sales of

$3,000.†

* If the model named here is not the one you want to use, press ) œ

and select the one you want.

† This result is not the same as it would be if SALES were the independent (x)

variable, and MINUTES were the dependent (y) variable.

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Weighted Mean and Grouped Standard Deviation

Data in one list (x) can be weighted or grouped (by frequency) by data

in another list (y). To find the mean of weighted data and the standard

deviation of grouped data:

1. Enter the data values―the x-variable―into a SUM list.

2. Enter the corresponding weights or frequencies―the y-variables―into

another list. (To calculate G.SD, the y-values should be integers.)

3. From the SUM menu, press E ) — to display a menu

of SUM-list names. The current list is ˜ unless named otherwise.

4. Press the menu key for the list of x-values.

5. Now select the list with the weights (or frequencies) (y).

6. To calculate the weighted mean, press ) Ÿ.

7. To calculate the grouped standard deviation, press .

Example: Weighted Mean. A survey of 266 one-bedroom rental

apartments reveals that 54 of them rent for $200 per month, 32 for

$205, 88 for $210, and 92 for $216. What is the average monthly

rent and its standard deviation?

Create two SUM lists. The first, called RENT, should contain the numbers

200, 205, 210, and 216, in that order. The second can be unnamed

and should contain the numbers 54, 32, 88, and 92, in that order.

Keys: Display: Description:

$ "

p s

;:H0L#T8U"

Clears current list or gets a

new one.

200 I

205 I

210 I

Stores rents into a list.

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216 I ;:H0L.T8U"

:E:198*%#&(("

e o

RENT I

;:H0L.T8U"

Names this list RENT. (See

page 30 to use the ALPHA

menu.)

p s ;:H0L#T8U" Gets a new, empty list.

54 I

32 I

88 I

92 I

;:H0L.T8U"

:E:198$''&(("

Stores frequencies into

second list.

e E

) —

FH9H7: X O12;1J9H"

Displays names of all

SUM lists.

2H<:" "FH9H7: @ O12;1J9H" Specifies RENT as the

x-list.

˜ 9;<H12" Specifies the current,

unnamed list as the y-list

and then displays the

FRCST menu. (Ignore

model type.)

) Ÿ $(,&++" Average monthly rent.

.&,-" Standard deviation of the

rents.

Summation Statistics

The summation values are of interest if you want to perform other

statistical calculations besides those provided by the calculator. To find

Σx, Σx2, Σy, Σy2, Σ(xy), and n, the number of elements in either list:

1. Display the FRCST menu and select the x- and y-lists as explained in

steps 1-4 of the instructions on page 134. To find the summation

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statistics for just one list of data, specify the same list for both x and y.

2. To see n, press ) ¡.

3. Press ) again to display the summation menu, and press the

menu label for the value you want.

Doing Other Calculations with SUM Data

If you would like to do other statistical calculations with SUM data

besides those in the CALC menu, you can do so by writing your own

Solver equation. There are Solver functions that can access data stored

in SUM lists, and there is a summation function that can combine all or

part of the values stored in specific lists.

Refer to “Accessing CFLO and SUM Lists from the Solver” in chapter 12.

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Time, Appointments, and

Date Arithmetic

The calculator contains a clock and calendar in the TIME menu. You can

select a 12-hour or 24-hour clock, and a month-day-year or day-

month-year calendar. You can:

! Record appointments that set alarms with optional messages.

! Determine the day of the week for a particular date.

! Calculate the number of days between two dates using the 360-day,

the 365-day, or the actual calendar.

Viewing the Time and Date

To view the time and date, press Y in the MAIN menu.

If you overwrite the time and date, you can restore them to the display

by pressing C.

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The TIME Menu

FIN BUS

CALC

APT1

SUM

APPT

APT2

TIME

ADJST

SOLVE

SET

APT10

CURRX

Table 11-1. The TIME Menu Labels

Menu Label Description

E !

Displays the CALC menu, for calculating the day of

the week and other date arithmetic.

§ !

Displays the APPT menu for setting and viewing

appointments.

¨ !

Displays the ADJST menu for adjusting the clock

setting.

Displays the SET menu for setting the time and date,

and for selecting the time and date formats.

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Setting the Time and Date (SET)

Table 11-2. The SET Menu Labels

Menu Label Description

Z Sets the date to the displayed number (MM.DDYYYY

or DD.MMYYYY).

Y Sets the time to the displayed number (HH.MMSS).

[ Switches between AM and PM (12-hour clock).

\ Switches between month/day/year and

day.month.year formats.

] Switches between 12-hour and 24-hour clock

formats.

^ Displays the formats for entering the clock’s date and

time.

To set the time:

1. Press Y © to display the SET menu.

2. Key in the correct time in the current format (1 or 5 indicates the

12-hour clock). For example, for 9:08:30 p.m. enter 9.0830 in a

12-hour clock or 21.0830 in a 24-hour clock.

3. Press Y to set the new time.

4. For 12-hour format: press [ to switch between AM and PM.

To set the date:

1. Key in the correct date in the current format. For example, for April 3,

2003 enter 4.032003 in month/day/year format or 3.042003 in

day.month.year format.

2. Press Z.

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Example: Setting the Date and Time. Set the date and time to April 5,

2003, 4:07 p.m.

Keys: Display: Description:

4.052003

F1: (+?(.?(% time"Sets date.

4.07 Y

[

F1:"

(+?(.?(% (+I(-Ixx5"

Sets time. Press [ if

necessary.

Changing the Time and Date Formats (SET)

Use the SET menu to change the time and date formats. To switch

between the 12- and 24-hour clocks, press ]. To switch between

the month/day/year and day.month.year calendars, press \.

Adjusting the Clock Setting (ADJST)

The ADJST menu adjusts the time setting forward or backward in

increments of hours, minutes, or seconds.

1. Press Y ¨.

2. Press the appropriate menu key(s) until the correct time is displayed.

For example, if the current time setting is 11:20:xx AM (ignoring

seconds), pressing _ twice changes the time to 1:20 PM. Then,

pressing ` three times changes the time to 1:17 PM.

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Appointments (APPT)

You can record up to ten appointments, each with an alarm. An

appointment can contain a message. You can also create repeating

appointments―appointments that recur at regular intervals.

APT1

DATE

APPT

APT2

TIME A/PM MSG RPT

MORE APT9 APT10

HELP

for each a

ointment

Viewing or Setting an Appointment (APT1-APT10)

Table 11-3. Menu Labels for Setting Appointments

Menu Label Description

Z Sets the appointment date.

Y Sets the appointment time, and automatically

enters the current date (if the existing appointment

date was in the past).

[ Sets AM or PM for 12-hour clock.

a Displays the ALPHA menu and any existing

message.

b Displays the existing repeat interval and the menu

for changing the repeat interval.

^ #

Displays the format for entering the date and time.

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To set an appointment or view its current setting:

1. Press Y, then §. The display tells you which appointments

(numbered 1-10) are set and which are past due (expired with

unacknowledged alarms).

Pressing

) displays the status and menu labels for appointments

6 through 10.

2. Press a menu key ― c through d. The display shows the

current appointment, if any, and the menu labels for setting

appointments.

3. Optional: press @c to remove any old information.

4. Setting the appointment time: Use 12-hour or 24-hour time, as

appropriate. Key in the time as a number in the form HH.MM. For

example, 2:25 p.m. would be 2.25 (12-hour format) or 14.25

(24-hour format). Press Y. The date is automatically set to the

current date if the existing date is in the past or was cleared.

For 12-hour format: press [ to switch between AM and PM.

5. Setting the appointment date: Key in the date in the current date

format. For example, enter October 4, 2003 as 10.042003

(month/day/year format) or 4.102003 (day.month.year format).

Press Z. If the appointment is within a year from today, you can

omit the year.

6. The appointment message (optional): To set, change, or just view a

Message Repeat interval

Menu for setting

appointments

ppointment number

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message, press a. Type the message (refer to page 30 for using

the ALPHA menu). Messages are limited to a maximum of 22

characters. Press I when done. (Press e to negate any

changes and retain the original message.)

7. The repeat interval (optional): To set, view, or change a repeat

interval, press b. Key in an integer and press the appropriate

key. For example, 2 e causes the appointment to go off at the

same time every other day; 90 ” sets the repeat interval to 1½

hours. f sets the appointment to non- repeating. You can

specify repeat intervals up to 104 weeks in length (728 days, 17,472

hours, etc.)

8. When done, press e to return to the APPT menu. The appointment

you just set will be recorded, such as FH:I#& You can check an

appointment by pressing its menu key (such as c).

C restores an appointment’s time and date to the display if it has

been overwritten by other operations.

Acknowledging an Appointment

To acknowledge the appointment and clear the message, press any key

(except @) during the beeping. Appointments not acknowledged within

20 seconds become past due.

When an appointment “comes due,” the alarm starts beeping and the

alarm annunciator ( ) is displayed, even if the calculator was off.*†

The message (or, if none, the time and date) is displayed.

* If the calculator is in the middle of a complex calculation when an

appointment comes due, the alarm annunciator comes on and the calculator

beeps once. When the calculation is done, the alarm goes off.

† The beeping can be suppressed or restricted to appointments. See “Beeper

On and Off,” page 36.

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Unacknowledged Appointments

An appointment not acknowledged during its alarm becomes past due.

The alarm annunciator remains on.

To acknowledge a past-due appointment:

1. Press Y §.

2. Press the menu key for the past-due appointment.

3. Press e to return to the APPT menu. The acknowledged

appointment is no longer listed as past due.

A repeating appointment is deactivated while it is past due and will not

go off subsequently until the past-due appointment has been

acknowledged.

Clearing Appointments

To cancel an appointment or to get rid of a repeating appointment, you

need to clear the appointment. Clearing changes the date and time to

00/00/00, 12:00 AM, and removes the message and the repeat

interval.

To clear an appointment, press the menu label for that appointment and

press @c

To clear all ten appointments, display the APPT menu (the menu with

c, g etc.) and press @c W.

Example: Clearing and Setting an Appointment. Today is Sunday,

April 20, 2003. You want to set appointment #4 to go off every

Tuesday at 2:15 p.m. to remind you of a staff meeting. Assume 12-hour

time format and month/day/year date format.

Keys: Display: Description:

Y § "Displays setting for

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h appointment #4.

@c +I ((?((?(( #$I((1"Clears appt. #4.

2.15 Y +I F4<"

(+?$(?(% $I#.1"

Stores appt. time and

supplies current date.

[ +I F4<"

(+?$(?(% $I#.5"

Sets appt. time to PM.

4.22 Z +I :4H"

(+?$$?(% $I#.5"

Stores appt. date.

STAFF I

+I :4H"

(+?$$?(% $I#.5"

Enters message: “staff”.

b 25:8<E<H" Displays RPT menu.

1 i 25:8# CHH3LFT"

+I :4H"

(+?$$?(% $I#.5"

Sets repeat interval.

e FH:I+" Returns to APPT menu

Appt. 4 is “set.”

Date Arithmetic (CALC)

The CALC menu performs date arithmetic:

! Determines the day of the week for any date.

! Determines the number of days between dates using one of three

calendars―actual, 365-day, or 360-day.

! Adds or subtracts days from a date to determine a new date.

The calendar for date arithmetic runs from October 15, 1582 to

December 31, 9999.

To display the CALC menu, press Y, then E.

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Table 11-4. CALC Menu Labels for Date Arithmetic

Label

Description

Stores or calculates a date. Also displays the day of

the week. If you omit the year, the calculator uses the

current year.

¬ Stores or calculates the number of actual days

between DATE1 and DATE2 , recognizing leap years.

- !

Calculates the number of days between DATE1 and

DATE2 using the 360-day calendar (30-day months).

® Calculates the number of days between DATE1 and

DATE2, using the 365-day calendar, ignoring leap

years.

¯ A shortcut: recalls the current date, which can then be

stored in DATE1 or DATE2.

The calculator retains the values for the TIME CALC variables DATE1,

DATE2, DAYS until you clear them by pressing @c while the

CALC menu is displayed.

To see what value is currently stored in a variable, press R menu

label

Determining the Day of the Week for Any Date

To find the day of the week for any date, key in the date and press

ª or «.

Calculating the Number of Days between Dates

To calculate the number of days between two dates:

1. Key in the first date (for today’s date, use ¯ ) and press ª.

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2. Key in the second date and press «.

3. Press ¬, -, or ® to calculate the number of days

using that calendar.

Example: Calculating the Number of Days between Two Dates. Find

the number of days between April 20, 2003 and August 2, 2040, using

both the actual calendar and the 365-day calendar. Assume the date

format is month/day/year.

Keys: Display: Description:

Y E "Displays CALC menu.

4.202003

A1:H#8"

(+?$(?$((% F4<"

Stores Apr. 20, 2003

as first date and

displays its day of the

week.

8.022040

A1:H$"

8(*?($?$(+( :M4"

Stores Aug. 2, 2040 as

second date.

¬ 17:419 A1@F8"

#%K'#,&(("

Calculates actual

number of intervening

days.

® %'. A1@F8#%K'(,&((" Calculates number of

intervening days by a

365-day calendar.

Calculating Past or Future Dates

To calculate a date a specified number of days from another date:

1. Key in the known date (for today’s date, use ¯ ) and press

ª.

2. Key in the number of days. This number should be negative if the

unknown date precedes the known date. Press ¬.

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3. Press «.

This calculation always uses the actual calendar.

Example: Determining a Future Date. On February 9, 2003, you

purchase a 120-day option on a piece of land. Determine the expiration

date. Assume the date format is month/day/year.

Keys: Display: Description:

Y E "Displays CALC menu.

2.092003

A1:H#8"

($?(,?$((% F4<"

Stores Feb. 9, 2003.

120 ¬ 17:419

A1@F8#$(&(("

Stores number of days into

the future.

« A1:H$8"

('?(,?$((% 0E<"

Calculates expiration date

(DATE2).

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The Equation Solver

The Equation Solver (the SOLVE menu) stores equations that you enter

and creates menus for them. You can then use those menus to do

calculations. Enter Solver equations in algebraic form regardless of the

calculation mode (ALG or RPN).

The Solver can store many equations―the number and length of

equations is limited only by the amount of memory available. The

equations are stored in a list.

FIN BUS

CALC

SUM

EDIT

TIME

DELETE

SOLVE

NEW

CURRX

Solver Example: Sales Forecasts

Suppose part of your job includes making sales forecasts, and that these

forecasts are revised based on new information. For instance,

! A change in the price of the product will affect sales by a forecasted

percentage, A%.

! A change in sales-force training will affect sales by a forecasted

percentage, B%.

! A competitor’s new product will affect sales by a forecasted

percentage, C%.

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Regardless of how you do this calculation (even if you do it longhand),

you are using an equation:

Next Forecast = Old Forecast + Change in Old Forecast

= Old Forecast + (Projected Percentage Changes

xOld Forecast)

or:

NEXT = OLD + ((A% + B% + C%) ÷ 100 x OLD)

Using the SOLVE and ALPHAbetic menus, you can type in this equation

<HX:8E9A)L16)J6)76TD#((BE9A"

and then automatically create this menu ―which contains all the

variables’ labels―by pressing I E :*

Each menu label represents a variable. You can use them to store and

calculate values the same way you use other menus and their built-in

variables.

Entering a Solver Equation. To type this equation, you must use the

ALPHA menu. If you are not familiar with the ALPHAbetic menu, refer to

“ Typing Words and Characters ” on page 30.

Keys: Display: Description:

& / !

:@5H HY41:;E<Q"

V;<54:W"

Displays SOLVE menu,

then ALPHA menu.

NEXT = OLD "The equation is too long

* Because the Solver uses arithmetic priority (B, D before ), /), a second set of

parentheses (before A% and after the second OLD) is not necessary. See

“Order of Calculations,” page 165.

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+( A %+

B %+ C %

)/ 100 *

OLD

>A)L16)J6)76T"

D#((BE9A"

for the display.

I <HX:8E9A)"

L16)J6)76TD#>"

Enters equation into list.

* #

C C #

>A)L16)J6)76T"

D#((BE9A"

Controls view of full

equation.

e <HX:8E9A)"

L16)J6)76TD#>"

Displays SOLVE menu.

Calculating with the Solver. Suppose last month’s forecast for a

product was 2,000 units. In the meantime, three market changes have

occurred that affect this forecast. A) The price of the product has

dropped, causing an expected 20% increase in sales. B) A major

sales-force training program started, causing an expected 5% increase

in sales. C) A competitor is introducing a new product, causing an

expected 15% drop in sales. Calculate the new forecast for next month.

Menu Label: Display: Description:

E OH2;G@;<=

HY41:;E<"

Verifies that equation is

valid; creates Solver menu

with menu labels for this

equation.

2000 M E9A8$K(((&((" Stores old forecast.

20 "

16" 168$(&((" Stores effect of price drop

on sales.

5 "

J6" J68.&((" Stores effect of sales-force

training on sales.

156 12: The Equation Solver

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15 & "

76" 768/#.&((" Stores effect of

competitor’s new product

on sales.

b <HX:8$K$((&((" Calculates new forecast

for next month.

Suppose your boss wants next month’s forecast to be 2,300 units. You

can’t affect A% or C%, but you can affect B% through the sales training

program. Determine what B% must be for NEXT to equal 2,300 units.

All you need to do is re-enter the one value you are changing:

Keys: Display: Description:

2300 b <HX:8$K%((&(("

J6" J68#(&((" The training program

would need to result in a

10% increase in sales to

effect a new forecast of

2,300.

The SOLVE Menu

If the Solver list is empty, you will see an instruction for entering an

equation when you press &:

If the Solver list is not empty, you will see the current equation—the last

one entered or selected.

Pressing [, ], @[, and @] moves you through the list.

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Table 12-1. The SOLVE Menu Labels

Label

Description

E Verifies the current equation and creates menu labels

for it. This is necessary before doing any calculations.

* Accesses the ALPHA-Edit menu (page 31) so you can

alter the current equation. The arrow keys move long

equations across the display.

n Deletes the current equation or just its variables (that is,

the space allotted in memory for the variables).

/ Allows you to enter a new equation.

While you’re working with a specific equation in the Solver, the

equation’s own menu appears in the display. To retrieve the primary

SOLVE menu, press e.

Entering Equations

To make an entry into the Solver list:

1. Press & /. (To insert the new entry at the bottom of the list,

press @].)

2. Use the ALPHA menu to type in characters (see page 30), and use the

regular keyboard to type in digits and arithmetic operators (+, =, yx,

etc.). If you make a mistake, use < to backspace or C to start

over. Or press e to bring up the ALPHA-Edit menu.

3. Press I to store the equation.

4. Press E to verify that the equation is valid, and to create its

menu labels. You now can proceed with your calculations.

When you press E the calculator displays:

OH2;G@;<= HY41:;E<>"

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while the Solver checks that the equation is mathematically valid.

(However, the Solver has no way of checking whether the equation is

the right one for your problem.) If the equation cannot be solved, the

calculator briefly displays:

;<O19;A HY41:;E<"

and the cursor will blink at the first character that the Solver could not

interpret. (It is possible that your mistake is somewhere else, but this is a

good place to start looking, since this is where the Solver got stuck.) The

ALPHA-Edit menu appears so you can make changes.

Check to be sure you’ve made no typing mistakes, and that you’ve

followed the rules for writing equations given on page 166 under

“What Can Appear in an Equation.”

An entry that is not an equation will be stored when you press I ,

but it cannot be verified when you press E.

Calculating Using Solver Menus (CALC)

If pressing E creates a Solver menu for your equation, then the

equation is good (that is, mathematically valid).

If the equation contains more than six variables, the Solver uses the label

) to switch between sets of menu labels.

Calculator line

Solver menu

To test whether your equation is in fact correct, test it out by entering

some values for which you already know the result, and see if the

Solver’s result is correct.

To do a calculation using a Solver menu:

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1. Store values in all but one of the variables (for example, 2000

M, etc.). Remember that you can verify stored values by pressing

R menu label.

2. To start the calculation, press the menu key for the variable you want

to calculate.

In most cases, this is all you need to know about how the Solver works.

However, certain types of equations are more difficult to solve.

If, during the calculation, the display temporarily shows two lines of

changing numbers, such as

1I#&.(((((((((( /"

1I#&#%+-'#$,*%+ )"

then the Solver is searching for a result for the variable A. Read the

section, “How the Solver Works,” starting on page 179.

Example: Return on Equity. The Return on Equity of a business can be

defined as:

ROE＝−−Operating income Interest Taxes

Common equity

Find the ROE of a small firm with $2,000 in assets. The assets earned

10% while its debt cost it 8%. The assets were financed using $500 of

common equity and $1,500 of debt. The firm paid no taxes.

Operating income＝assets × percentage earnings on assets

＝1FFH:B6H2<

Interest＝debt × percentage interest paid on debt

＝AHJ:B6;<:

Common equity＝amount of common equity used for financing

＝HY:@

The Solver equation would be:

2EH8L1FFH:B6H2<D#((/AHJ:B6;<:D#((/:1XTDHY:@B#(("

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Keys: Display: Description:

@A "Restores MAIN menu.

& / :@5H HY41:;E<Q"

V;<54:W"

Displays ALPHA menu.

ROE =

( ASSET *

% ERN

- DEBT *

% INT

- TAX )

/ EQTY

>/AHJ:B6;<:/:1XT"

DHY:@"

Entering the equation.

I 2EH8L1FFH:B6H2<"

/AHJ:B>"

Stores the equation.

E "Verifies the equation and

displays the menu labels

for ROE, ASSET, %ERN,

DEBT, %INT, and (press

)) TAX and EQTY.

2000 "

1FFH:"

10 "

6H2<"

1500 "

AHJ:"

8 "

6;<:"

) 0

:1X"

500 "

HY:@"

1FFH:8$K(((&(("

6H2<8#(&(("

AHJ:8#K.((&(("

6;<:8*&(("

:1X8(&(("

HY:@8.((&(("

Stores the values for the

assets, the percentage

earnings on assets, the

amount of debt, the

percentage interest paid

on the debt, the taxes

paid, and the common

equity.

) #

2EH" #

2EH8#'&(("

The return on equity is

16%.

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Editing an Equation (EDIT)

If you have an ;<O19;A HY41:;E<, the cursor stops over the first

character that the Solver could not logically interpret.

You can alter the current equation using the ALPHA-Edit menu:

1. Press * to access the ALPHA-Edit menu. (See “Editing

ALPHAbetic Text,” page 31.) You can use < (backspace) and C

(clear), as well.

2. To insert letters, press D and the appropriate letters. Press e

to bring back the editing menu.

3. Press I to replace the previous version with the edited version.

Editing an equation clears its variables.

To abort an editing operation without saving any of the changes, press

Naming an Equation

Naming equations helps you identify them later. The name precedes the

equation, separated by a colon. If you don’t name an equation initially,

you can name it later using *.

Type the name just as you type the rest of the equation. The calculator

knows that whatever comes before the colon is not part of the equation.

The name is for your visual aid only; the calculator cannot recognize it.

Names can be any length and contain any character except ＋－ x ÷ ( )

＜＞ ^ ：＝ space

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Finding an Equation in the Solver List

To display an entry in the Solver list, display the SOLVE menu and move

through the list using the [ and ] keys. @[ moves to Z:E5 EG

9;F:[ and @] moves to ZJE::E0 EG 9;F:[.

Shared Variables

If two or more equations contain the same variable, that variable is

shared among those equations. For example, suppose your Solver list of

equations includes these two equations labeled RUG, which figures the

cost of a carpet, and TOTAL, which figures the total cost of buying a

carpet and installing it:

24=I 5?@AB9BCD,87EF:"

:E:19I 7EF:)ME42FB$(&.(87M12=H"

COST is a shared variable. You can calculate a value for COST using

the RUG equation, then switch to the TOTAL equation and calculate

CHARGE after entering HOURS. Since the value for COST is shared,

you do not need to store it again.

No sharing occurs between variables outside the Solver and those

within the Solver. For example, this COST variable in the Solver is not

shared with the COST variable in the MU%C and MU%P menus in BUS.

To transfer values between built-in variables and Solver variables, store

them into storage registers. Recall them after switching menus.

Remember that the value in the calculator line stays there when you

switch menus.

Clearing Variables

You can clear the variables in a Solver equation just as you clear

variables in other menus: press @c while the menu with those

variables is displayed.

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Make sure that the menu for the variables is in the display. (The

equation itself should not be in the display. If it is, press E.)

Pressing @c now sets NEXT; OLD, A%, B%, and C% to zero.

Variables are also cleared when their equation is edited.

If the SOLVE menu is displayed (rather than the SOLVE CALC

menu), then pressing @c will prompt AH9H:H 199

O12;1J9HFU. Press X, otherwise you will lose the

variables in all the equations. (See “Deleting All Equations or

Variables in the Solver,” page 164.)

Deleting Variables and Equations

Each equation in the Solver list uses calculator memory to store 1) itself,

and 2) its variables.*

Deleting a variable is quite different from clearing it:

! Clearing a variable sets it to zero; the variable retains its storage

location in memory. This does not save memory space.

! Deleting a variable erases its value and its storage location. This is a

way to save memory space. If a variable is shared, its value is lost to

all equations that share it. The memory space for a deleted variable is

re-created the next time you use that equation.

* An equation that has not been verified (E pressed) does not have any

variables allocated to it. Therefore, it has no variables to be cleared or

deleted.

Note

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Deleting One Equation or Its Variables (DELET)

To delete an equation or its variables:

1. Display the equation.

2. Press j in the SOLVE menu.

3. To delete the equation, respond W to both questions:

AH9H:H :MH O12;1J9HFU"

AH9H:H :MH HY41:;E<U"

(If the entry has no variables allocated, then only the second question

appears.)

4. To delete just the variables, respond X to

AH9H:H :MH HY41:;E<U. This preserves the equation.

Deleting All Equations or All Variables in the Solver

(@c)

To delete all the equations in the Solver, or just all the variables in all the

equations:

1. Display the SOLVE menu. It doesn’t matter which equation is

displayed.

2. Press @c. To delete all equations, respond W to both

questions:

AH9H:H 199 O12;1J9HFU"

AH9H:H 199 HY41:;E<FU"

3. To delete just the variables, respond X to

AH9H:H 199 HY41:;E<FU. This preserves all equations.

Writing Equations

An equation in a book looks different from an equation in the Solver. A

numerator and denominator might be separated by a bar, such as

12: The Equation Solver 165

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−×

abc

def

Since a Solver equation appears all on one line, you must group the

numerator and denominator separately by using parentheses, such as

L1)J)7TDLA/HBGT"

Order of Calculations. Operations occur from left to right but do:

! Exponentiation first. For example, 1BJ\%87 is interpreted as A ×

B3 = C. B is raised to the 3rd power and then multiplied by A. To

raise A × B to the 3rd power, write the equation as L1BJT\%87.

! Multiplication and division before addition and subtraction. For

example, 1)JD78#$ is interpreted as A + ( B/C ) = 12. To divide

the sum of A + B by C, enter the equation as L1)JTD78#$.

Parentheses. Parentheses override the above rules of priority. When in

doubt, use parentheses. It never hurts to use parentheses―even multiple

parentheses. (Do not use brackets or braces.)

For example, earlier (page 154) we used the equation

Next Forecast＝Old Forecast +

()

++ ×





%% %Old Forecast

100

ABC

which was entered into the calculator as

<HX:8E9A)L16)J6)76TD#((BE9A.

would be entered as 1DLJB7T&

+×

ADE

could be entered as 1)JB7DLABHT&"

166 12: The Equation Solver

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++×

(5)

ADE

could be entered as 1)JB7DLLA).TBHT&"

What Can Appear in an Equation

Long Equations. There is no limit on the length of an equation (or the

number of variables it has) if there is enough memory to store it. An

equation longer than one display line (22 characters) moves to the left

and adds an ellipsis (...).

To view a long equation, move the cursor using the arrow keys on the

ALPHA-Edit menu. For example:

:E:197EF:89H<=:MBC;A:MBMH;=M:D#$B4<;:BL#)0123456D#((T

looks like

:E:197EF:89H<=:MBC;A:>"

when it is stored. Press * C C to view successive

portions of the equation:

>MBMH;=M:D#$B4<;:BL#)>"

Spaces. You can use as many spaces as you like between variables,

operators, and numbers.

Names of Variables. A variable’s name can be up to 10 characters

long, but cannot contain the characters ＋－ x ÷ ^ ( ) ＜＞＝： space

The first three to five characters (depending on their widths) become the

variable’s menu label. Therefore, make sure no two variables in the

same equation have the same first three to five characters.

Do not use AND, NOT, OR, XOR, or PI as variable names because they

will be interpreted as functions.

Numbers (Constants). Do not put commas or other characters in

numbers. For instance, type #(((( for ten thousand (not N#(K((().

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Parentheses. Do not use brackets or braces. Parentheses determine

order, but do not imply multiplication. For example, the equation Psn ＝

Ps (1－F) would be typed into the Solver as 5F<85FBL#/GT. The ×

sign must be inserted between 5F and the parenthesis.

Functions and Conditional Expressions. An equation can contain any

of the functions and conditional expressions given in the table on pages

168-171. Some of these functions also have typing aids.

Math Operators (“Typing Aids”). All of the math operators are located

either on the keyboard (/, @t, etc.) or in the MATH menu ( 3,

I, etc.). Any of these operators except % can be included in an

equation. (In the Solver, 6 is just a character.) You can call up the

MATH menu from the Solver.

Many of these operators look different in an equation: pressing @v

produces FY2:L , for example. You then supply a number or variable

followed by a closing parenthesis. The list of Solver functions on pages

168-171 shows the spelling of each function. Note that you supply the

number after supplying the function.

You can also type these functions letter by letter using the ALPHA menu.

However, it is faster to select math operators directly on the keyboard or

in the MATH menu. This is called a typing aid.

For instance, these two methods of placing 25! (factorial) into an

equation are equivalent. Starting after & /:

1. Using the ALPHA Menu

Keys: Display: Description:

° !"

± G"

, "

- G1"

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, "

: G17"

< "

> G17:"

( 25 )= G17:L$.T8"

G17:L$.T81"

This calculates 25!

(factorial).

2. Using a Typing Aid

Keys: Display: Description:

@m "MATH menu labels

appear.

4 #G17:L" The ALPHA menu

automatically returns after

one MATH selection.

25 )= G17:L$.T8"

G17:L$.T81"

This also calculates 25!,

and with fewer

keystrokes.

Solver Functions

Here is a complete list of functions that you can include in Solver

equations. The items inside parentheses must be replaced by specific

numbers, variables, or algebraic expressions.

In addition, you can use the arithmetic operators (＋, －, x, ÷ , yx), but

not %. (In the Solver, 6 is just a character, not an operator.)

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Table 12-2. Solver Functions for Equations

Function Description

ABS(x) Absolute value of x.

ALOG(x) Common (base 10) antilogarithm;

10x.

CDATE Current date.

CTIME Current time.

DATE(d1:n) The date n days after (when n is

positive) or before (when n is

negative) date d1. The format for d1

is set in the TIME/SET menu.

DDAYS(d1:d2:cal) Number of days between dates d1

and d2. Formats for d1 and d2 are

set in the TIME menu; cal designates

the calendar:

! cal ＝ 1 for the actual calendar,

which recognizes leap years.

! cal ＝ 2 for the 365-day

calendar, which ignores leap

years.

! cal ＝ 3 for the 360-day

calendar, which uses 12, 30-day

months.

EXP(x) Natural antilogarithm; ex.

EXPM1(x) ex－1.

FACT(x) x!; factorial of a positive integer.

FLOW(CFLO-listname:flow#) Value of the specified cash flow.

FP(x) Fractional part of x.

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Table 12-2. Solver Functions for Equations (Continued)

Function Description

HMS(time) Converts time in decimal hours to

HH.MMSS format.

HRS(time) Converts time in HH.MMSS format to

decimal hours.

IDIV(x:y) Integer part of the quotient of x/y.

IF(cond:expr1:expr2) Conditional expression: if cond is true,

use expr1; if cond is false, use expr2.

See page 174.

INT(x) Greatest integer less than or equal to x.

INV(x) Inverse of x; 1/x.

IP(x) Integer part of x.

ITEM(SUM-listname:item#) Value of the specified SUM-list item.

LN(x) Natural (base e) log of x.

LNP1(x) In (1 + x)

LOG(x) Common (base 10) log of x.

MAX(x:y) Compares x and y, and returns the

larger of the two.

MIN(x:y) Compares x and y, and returns the

smaller of the two.

MOD(x:y) Remainder of the division x/y.

MOD(x,y) = x－y x INT(x/y)

PI π ; 3.14159265359 (12 digits).

RND(x:y) Rounds x to y decimal places if 0 ≤ y ≤

11, or rounds x to y significant digits if

－12 ≤ y ≤－1. y must be an integer.

S(variable name) Used in an IF function to test if solving

for the variable named. Used to

combine related equations into one

Solver menu. See page 178.

SGN(x) Sign of x (＋1 if x > 0, 0 if x＝0, －1 if

x < 0.

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Table 12-2. Solver Functions for Equations (Continued)

Function Description

Σ(cfr:c1:c2:s:expr) Summation of the algebraic expression

expr for values of the counter ctr,

stepping from c1 to c2 at increments of s.

See page 176.

SIZEC(CFLO-listname) The number of the last flow in specified

CFLO list.

SIZES(SUM-listname) The number of items in specified SUM

list.

SPFV(i%:n) Future value of a single $1.00 payment;

equivalent to (1 + i% ÷ 100)n. n is the

number of compounding periods. i% is

the interest rate per compounding

period, expressed as a percentage.

SPPV(i%:n) Present value of a single $1.00

payment; equivalent to 1 ÷ SPFV(i%:n).

n is the number of compounding

periods. i% is the interest rate per

compounding period, expressed as a

percentage.

SQ(x) Square of x ; x2.

SQRT(x) Square root of x ; X.

#T(CFLO-listname:flow#) The number of times that specified cash

flow occurs.

TRN(x:y) Truncates x to y decimal places if 0 ≤ y

≤11, or truncates x to y significant digits

if －12 ≤ y ≤－1. y must be an integer.

USFV(i%:n) Future value of a uniform series of

$1.00 payments; equivalent to

(SPFV(i%:n)－1) ÷ (i% ÷100). n is

number of payments. i% is periodic

interest rate, expressed as a

percentage.

USPV(i%:n) Present value of a uniform series of

$1.00 payments; equivalent to

USFV(i%:n) ÷ SPFV(i%:n). n is number of

payments. i% is periodic interest rate,

expressed as a percentage.

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Example Using a Solver Function (USPV): Calculations for a Loan

with an Odd First Period. Suppose an auto purchase is financed with a

$6,000 loan at 13.5% annual interest. There are 36 monthly payments

starting in one month and five days. What is the payment amount?

Use the following formula when the time until the first payment is more

than one month but less than two months. Interest for this odd

(non-integer) period is calculated by multiplying the monthly interest by

the number of days and dividing by 30.

The formula for this loan is:

−



−+









+× + =









1 1

1200

1 0

1200 30

1200

ANNI

ANNI DAYS

PV PMT ANNI

where:

ANNI＝ the annual percentage interest rate.

N＝ the number of payment periods.

DAYS＝ the number of leftover, odd days (an integer from 0 through

30).

PV＝ the amount of the loan.

PMT＝ the monthly payment.

The formula can be rearranged and simplified using USPV, the Solver

function for returning the present value of a uniform series of payments:

5OBL#)1<<;D#$((BA1@FD%(T)"

50:B4F5OL1<<;D#$I<T8("

The keystrokes are:

PV *( 1 + ANNI / 1200 * DAYS / 30 )

+ PMT * USPV ( ANNI / 12:N )= 0

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Keys: Display: Description:

& @]

ZJE::E0 EG 9;F:[" Displays SOLVE menu and

bottom of Solver list.

/ :@5H HY41:;E<Q"

V;<54:W"

Displays ALPHA menu.

(type in

equation as

shown above)

&&&0:B4F5OL1<<;D"

#$I<T8("

Remember that the colon is

located after. .

(Press 2 . ²)

(&((" Enters equation, verifies

it, and creates menu.

6000 V 5O8'K(((&((" Stores loan amount in

PV.

13.5 "1<<;" 1<<;8#%&.(" Stores annual percent interest

in ANNI.

5 ¬ A1@F8.&((" Stores number of odd days in

DAYS.

36 T <8%'&((" Stores number of payments in

W 50:8/$(%&,," Calculates monthly PMT of

$203.99.

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Conditional Expressions with IF

Equations can include conditional expressions using the function IF. The

syntax of the IF function is:

IFLconditional expression I algebraic expression I algebraic expressionT *

For example, the solver accepts the equation:

JE<4F8;GLF19HF[%(((I&($ B F19HFI&(# B F19HFT"

According to this equation, if SALES is greater than 3000, then the

BONUS equals .02 × SALES; otherwise (“or else”), BONUS equals

.01 × SALES.

Logical Operators. Four logical operators can be used in conditional

expressions: AND, OR, XOR, and NOT.

Relational Operators. Six relational operators are available for

conditional expressions.

Operator Keys

＞

＜

＝

≥

≤

≠

³ (ALPHA menu)

´ (ALPHA menu)

³ =

´ =

´ ³

* A conditional expression that contains within it an algebraic expression might

cause the error ;<O19;A HY41:;E<. If this happens, insert a ) before the

left parenthesis starting the algebraic expression. For example, change

;GLL1)$TD.Z#$I&&&to

;GL)L1)$TD.Z#$I&&&.

then or else

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Examples of Conditional Equations.

! J = ;G L1[- 1<A 1Z8#.I$B1D'I%B1)#(T)7

Means: If A is greater than 7 and is less than or equal to 15, then

B＝ 2 x A ÷ 6＋C. Otherwise, B＝3 x A＋10＋C.

! O194H 8 G;2F:);GL<E:LG;2F:8(TI#DG;2F:I(T

Means: If FIRST is not equal to 0, then

VALUE＝FIRST＋1 ÷ FIRST. If FIRST＝0, then VALUE＝FIRST.

! : 8 C"B;GL18( XE2 J8(I1)JI1]JT

Means: If A or B, but not both, equals 0, then T＝W x (A + B).

Otherwise, T = W x A x B. In other words,

When A＝0 and B≠0, T＝W x B.

When A≠0 and B＝0, T＝W x A

When A＝0 and B＝0, T＝0.

When A≠0 and B≠0, T＝W x A x B.

Example: Nested IF Functions. An IF function can be used as the

argument of another IF function. This is called nesting. Suppose a

corporation uses a rating system to determine salary. Employees are

rated on a scale from 1 through 3, and are given the following annual

percent raise based on their rating:

Rating Percent Salary Increase

10%

The Solver equation to calculate an employee’s new salary is based on

his or her rating and old salary. What would be the new annual salary

for an employee with a rating of 2 who currently earns $27,500

annually?

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Press & /, then enter the equation:

<HC8E9A"]"L#);GL28#I&(%I;GL28$I&('I&#TTT"

To do the calculation:

Keys: Display: Description:

"Stores, verifies, and

creates menu labels for

the equation.

27500 M E9A8$-K.((&((" Stores old salary.

2 R 28$&((" Stores rating.

/ <HC8$,K#.(&((" Calculates new salary.

The Summation Function (∑)

The Σ function does summation calculations in an equation:

^Lcounter variable I starting value I ending value I step size I

algebraic expressionT

The counter variable takes on a series of values, beginning with the

starting value, and incrementing according to the step size, until it

passes the ending value. For each value of the counter, the algebraic

expression is evaluated, and the value is added to the previous value.

The Σ function returns the final summation.

For example, when the equation:

FH2;HF8^L;I#I'I#I;BX\;T"

is solved for SERIES, the counter I runs from 1 through 6 in steps of one

―that is, 1, 2, 3, 4, 5, 6. For each value I, the expression ;BX\; is

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calculated and added to the sum. Thus the stored value of X is used to

calculate X + 2X2 + 3X3 + 4X4 + 5X5 + 6X6.

The following equation uses a variable as the ending value, 0 as the

beginning value, and a step size of 2.

FH2;HF8^L;I(I91F:I$I;BX\;T"

If 8 is stored in LAST, I takes on values of 0, 2, 4, 6, and 8. Then the

stored value of X will calculate 2X2 + 4X4 + 6X6 + 8X8.

Accessing CFLO and SUM Lists from the Solver

You can use a Solver equation to perform calculations other than those

in the CFLO and SUM menus using data stored in CFLO and SUM lists.

The following Solver functions gain access to these lists.

! F;_H7LCFLO-listnameT returns the number of the last flow in the

specified CFLO list. For example, if the last flow in the list INV were

G9ECL'T8.K(((&((, then F;_H7L;<OT would equal 6.00.

! G9ECLCFLO-listname I flow numberT returns the value of the

specified flow.

! P:LCFLO-listname I flow numberT returns the number of times the

specified flow occurs.

! F;_HFLSUM-listnameT returns the number of items in the specified

SUM list.

! ;:H0LSUM-listname I item numberT returns the value of the

specified item.

Summation of List Data. The Σ function can be used to sum calculations

done with numbers in lists. For example, the following equation

calculates Σxi2yi2 for values stored in two SUM lists named XVAR and

YVAR, which must have the same number of items:

FX$@$8^L;I#IF;_HFLXO12TI#I;:H0LXO12I;T\$B"

;:H0L@O12I;T\$T"

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“Chi-Squared Statistics” in chapter 14 illustrates another use of the Σ

function with SUM lists.

Creating Menus for Multiple Equations (S Function)

The S (solving for) function is used in conjunction with the IF function

to group related equations together and to specify the criteria for

choosing one of them to solve.

S(variable name)

The advantage over two separate equations is that the single equation

gives you a single menu with all possible variables. That way, if you are

working with two different but related problems, you can keep the same

Solver menu labels in the display all the time―you don’t have to switch

equations.

For example, consider these two equations for conversions:

3=B$&$#89J and 0B%&$*8G:"

The following, rearranged single equation can do either conversion:

;GLFL3=T E2 FL9JTI3=B$&$#/9JI0B%&$*/G:T8("

This means: if you are solving for either KG or LB, then use

KG × 2.21－LB＝0. Otherwise (that is, if you are solving for M or FT),

use M × 3.28－FT = 0. The two conversion equations are rewritten so

that all the variables appear on one side of each equation, and the

other side is set equal to zero.

The S function appears as part of the conditional expression of the IF

function. You can leave out the “＝0” and it will be understood that the

whole equation is set equal to zero.

Example: Unit Conversions. Use the above equation to convert

between kilograms and pounds and between meters and feet.

Press & / then enter the equation:

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;GLFL3=T E2 FL9JTI3=B$&$#/9JI0B%&$*/G:T"

Press I to store it, then E to verify it and create its menu:

1. Convert 225 pounds to kilograms.

Press 225 "

9J" "

3=" Result is 3=8#(#&*#.

2. How many feet equal 100 meters?

Press 100 "

0" "

G:" Result is G:8%$*&((&

Note that you do not have to clear variables between steps 1 and 2.

The S function considers only those values in the part of the equation

that it is solving.

How the Solver Works

The Solver has two ways of finding an answer. First, it tries to find a

direct solution by rearranging the equation and then solving for the

variable. If the Solver finds a direct solution, the calculator displays the

result.

If the Solver is unable to find a direct solution, it tries to find the answer

indirectly by iteration. It estimates a set of answers, sees how close they

are to a solution, and then makes another set of estimates. The

calculator displays the Solver’s current estimates as the Solver searches

for an answer. You should keep in mind that there might be more than

one solution to an equation, and that it might be necessary for you to

enter guesses to influence which solution the Solver finds. If the

displayed estimates don’t appear to be proceeding towards a number

you judge to be a reasonable answer, you can stop this iterative process,

enter your own guesses, and restart the search. (See “Halting and

Restarting the Iterative Search” and “Entering Guesses,” below.)

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The process of finding a solution iteratively is very complex. There are

four possible outcomes. Refer to “Solver Calculations” in appendix B for

additional descriptions of these outcomes.

! Case 1: The calculator displays a result. It is very likely that this is a

solution to the equation. To check how good this result is, you can

repeat the calculation by pressing the menu key for the variable you

solved for. If the two sides of the equation have not been calculated to

be exactly equal, the calculator displays a message with the values

for the left and right sides of the equation. Read “Solver Calculations”

in appendix B for an explanation of the meaning of this display.

! Case 2: The calculator displays a message with the calculated,

unequal values of the left and right sides of the equation. The Solver

has found a possible solution, but you must interpret its validity. To see

the questionable solution, press < or C. Refer to “Solver

Calculations” in appendix B for more information.

! Case 3: The calculator displays J1A =4HFFHFI 52HFF

V792W :E O;HC. The Solver cannot begin the search with the

current guesses. Press < or C to view the starting guesses. To

supply new guesses, see “Entering Guesses,” below.

! Case 4: The calculator displays FE94:;E< <E: GE4<A. Check

to see if your equation and stored values are correct. If the equation is

correct, you might be able to find a solution by entering very good

guesses.

Halting and Restarting the Iterative Search

When the Solver is iteratively searching for a solution (in other words,

when the Solver is displaying sets of estimates), you can halt the

calculation by pressing any key except @. The calculator displays the

message ;<:H2245:HA. To see the best estimate the Solver has

found so far, press C or <. You can restart the search from where

it left off by pressing the menu key for the variable you are solving for.

Or, you can restart the search using your own guesses (see “Entering

Guesses,” below).

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Entering Guesses

Entering your own guesses serves two purposes. First, it can save time

by telling the Solver where to start searching. Second, if more than one

solution exists, entering guesses may lead the Solver to a solution in a

specified range. The closer your guesses are to the desired solution, the

better chance the Solver has of finding it.

You can enter guesses at these times:

! Before beginning the calculation, after you’ve stored a value for every

variable except the unknown variable. If you enter one guess, the

Solver generates a second guess.

! After you’ve halted the iterative search.

! After the Solver has returned an answer, and you wish to begin

searching for another answer.

You can enter one or two guesses. If you enter one guess, the Solver

makes a second guess. If you enter two guesses, the Solver uses those

two guesses to start searching for a solution. The Solver works most

efficiently when the answer is between your two guesses. For example,

if you know the answer is between 5 and 12, you should enter 5 and

12 as the starting guesses.

To enter one guess, key in the value and press the menu key twice.

For example, 4.5 - - enters 4.5 as a guess for a Solver

variable named A and starts the calculation.

To enter two guesses, key in the first guess and press the menu key. Then

key in the second guess and press the menu key twice. For example, 0

- 100 - - causes the Solver to search for A using 0

and 100.

Example: Using Guesses to Find a Solution Iteratively. One equation

for calculating the profit from a manufacturing operation is:

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Profit ＝ (Price × Quantity) － (Variable costs × Quantity)

－ Fixed Costs

The C-Sharp Piano Corporation sells pianos for $6,000. Variable costs

are $4,100; fixed costs per year are $112,000. How many pianos

must C-Sharp sell this year in order to earn a profit of $130,000? (In

past years, C-Sharp has had to sell between 100 and 200 pianos to

make an acceptable profit. You can use this information as initial

guesses.)

Press & / , then enter the equation:

52EG;:852;7H ] Y:@/O127EF: ] Y:@/G;X7EF:"

Keys: Display: Description:

I E "Stores, verifies, and

creates labels for the

equation.

6000 * 52;7H8'K(((&((" Stores price.

4100 "

O127E"

112000 "

G;X7E"

130000 "

52EG;"

O127EF:8+K#((&(("

G;X7EF:8##$K(((&(("

52EG;:8#%(K(((&(("

Stores variable cost,

fixed cost, and profit.

The following steps enter guesses for QTY. If the Solver must search

iteratively to solve for QTY, it will begin by using the estimates 100 and

200.

Keys: Display: Description:

100 "

Y:@" Y:@8#((&((" The first guess for QTY.

200 "

Y:@" Y:@8$((&((" The second guess for

QTY.

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Y:@" Y:@I$((&(((((((((/"

Y:@I#((&((((((((()"

Y:@8#$-&%-"

Solves for QTY iteratively.

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Printing

The calculator can print information using the HP 82240 Infrared Printer,

which accepts the infrared signal from the printer port. This chapter

describes information you can print. Operation of the printer is covered

in the printer owner’s manual.*

Port

The print annunciator ( )appears in the display whenever the

calculator sends information through its printer port.

Because communication goes only one way―from calculator to printer

―the calculator cannot determine whether the printer is receiving

information. If a printing operation involves many lines of information,

the calculator slows its transmission rate to allow the printer time to print.

To preserve battery power, the calculator will not transmit data to the

printer when the low-power annunciator ( ) is on. If a low-power

condition occurs after you’ve started a printing operation, printing stops

and the calculator displays the message J1:: :EE 9EC :E 52;<:.

* Since the hp-17bII+ cannot send control characters to the printer, portions of

the printer’s manual pertaining to control codes and graphics characters do

not apply.

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The Printer’s Power Source

The speed of the printer depends on whether it is using its optional ac

adapter. To optimize printing performance, set the printing speed mode

in the calculator appropriately. To view or change the printing speed

mode:

1. Press @>.

2. Press . to change and display the new mode. If necessary,

press . again to set the desired mode:

! 52;<:H2I 17 1A15:H2

! 52;<:H2I <E 17 1A15:H2

3. Press e.

For long printing operations, printing will be faster using the printer’s ac

adapter and the calculator’s appropriate printing speed mode. When

the printer is powered by batteries alone, be sure to change the mode to

52;<:H2I <E 17 1A15:H2 so that the calculator will not transmit

data too rapidly.

Double — Space Printing

Press @> / to turn double-space printing on or off. Then

press e.

Printing the Display(P)

To print whatever is in the calculator line, press P. This prints

numbers, expressions, single Solver equations, and messages. Menus

cannot be printed.

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Printing Other Information (@p)

LIST STK REGS

PRINTER

TIME MSG TRACE

The PRINTER menu provides the ability to print most of the information

you’ve stored, including the contents of variables, lists, appointments,

the history stack, registers, and the current date and time. You can also

transmit descriptive notes to label the output. (To print amortization

schedules, see “Printing an Amortization Table,” page 81.)

From within any menu you can press @p to bring up the PRINTER

menu. This table summarizes those printing activities.

Table 13-1. The PRINTER Menu Labels

Menu Label Description

k #

Prints data stored or calculated in the current menu.

See “Printing Variables and Lists,” below.

l Prints the contents of the history stack.

m Prints the contents of registers 0 through 9.

Y Prints the current date and time.

a Displays the ALPHA menu for typing a message up to

22 characters long. See page 188.

n Switches between Trace On and Trace Off modes.

See “Trace Printing,” page 188.

Upon completion, all of these functions except n return the

previous menu to the display.

Printing Variables, Lists, and Appointments (LIST)

You can list specific sets of information stored in menus by pressing

@p k while the relevant menu labels are displayed.

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Printing the Values Stored in Variables. You can print a listing giving

the values of all variables whose menu labels are displayed.*

For example, if the calculator is in the FIN TVM menu, it displays the

labels T U V W X ..

Pressing @p k now produces a print-out like this:

<8" %'(&(("

;6@28" #$&.("

5O8" '.K(((&(("

50:8" /',%&(("

GO8" *&(("

5?@28" #$&(("

H<A 0EAH"

Printing Number Lists. To print out the contents of a particular SUM or

CFLO list, that list must be the current list. Pressing @p k

while a SUM list named SALES is the current list produces labeled output

like this:

M10HI F19HF"

;:H0P" O194H"

#" #K+((&(("

$" ,$(&(("

%" #K#((&(("

+" $K$'.&(("

:E:198" .K'*.&(("

Printing Solver Equations. To print one or all Solver equations, display

the main SOLVE menu (press &).

! To print just the current equation, press P.

! To print out the entire list of equations, press @p k.

* Except IRR%. Instead, press t P to print the value for IRR%.

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Printing Appointments. To print all stored appointments, display the

§ menu (press § then press @p k. This

produces a listing like this for each appointment:

#I CHA (-?$%?(% #(I((1"

AH0E GE2 F0;:M"

25:8<E<H"

Menus Not Associated with Stored Data. Remember that many menu

labels do not represent data, but rather activities, such as " ,

#, n and ©. They contain no information for printing.

The calculator beeps if there is nothing to print when you press

@p k.

Printing Descriptive Messages (MSG)

You can include descriptive messages with your printed output by using

a. For example, suppose you wanted to print a number that

represents the balance for September. You could start the output with the

label “SEPTEMBER BALANCE”.

1. Press @p, then a. This brings up the ALPHA menu.

2. Type (and edit) the label or message.

3. Press I to print out the label or message.

Now print out the number itself (if it’s in the calculator line, press P).

Trace Printing (TRACE)

Trace printing produces a record of all the keys you’ve pressed and of

calculated results. When tracing is off, use P and @p to print

what you want. When tracing is on, the calculator uses more power and

operates more slowly.

To switch trace printing on and off:

1. Press @p.

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2. Press n to change the setting. A message informs you that

tracing is on or off. If necessary, press n again to display the

desired message.

3. Press e.

Example: Trace-Printing an Arithmetic Calculation. Produce a record

of the keystrokes you use to do the following calculation and store the

result in the TVM variable PMT.

1/12× 4,800 + 125

Press @p n to set 52;<: 0EAHI :217H E<. If you

see 52;<: 0EAHI :217H EGG, press n again.

Keys: Print-out:

e HX;:"

" !G;<"

] :O0"

12 @t " #$&((" #?X"

(&(*" ```"

* B"

4800 + " +K*((&((" )"

125 = " #$.&((" 8"

.$.&(( ```

W 50:"

@p 52;<:H2"

n :217H"

e "

How to Interrupt the Printer

Pressing a calculator key during a printing operation will interrupt

transmission, but not immediately stop the printing.

To stop the printer immediately, turn it off.

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Additional Examples

Loans

Simple Annual Interest

See appendix F for RPN keystrokes for this example.

Example: Simple Interest at an Annual Rate. Your good friend needs a

loan to start her latest enterprise and has requested that you lend her

$450 for 60 days. You lend her the money at 7% simple annual interest,

to be calculated on a 365-day basis. How much interest will she owe

you in 60 days, and what is the total amount owed?

The interest is: (7% of $450) × 60 days

365 days

Keys: Display: Description:

450 * 7 % +.(&(( B(&(-" Annual interest.

* 60 / 365

.&#*)"

Actual interest for 60

days.

450 = +..&#*" Add principal to get total

debt

A Solver Equation for Simple Annual Interest:

AHJ:89E1<)9E1<B;6D#((BA1@FD%'."

DEBT = the total owed at the end of the loan period.

LOAN = the original amount (principal) lent.

I% = the annual interest rate as a percent.

DAYS = the number of days in the loan.

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For instructions on entering Solver equations, see “Solving Your Own

Equations,” on page 29.

If you know the dates for the course of the loan, rather than the number

of days, use this for an actual-calendar basis:

AHJ:89E1<)9E1<B;6D#((BAA1@FLA1:H#IA1:H$I#TD%'."

or use this for a 360-day basis:

AHJ:89E1<)9E1<B;6D#((BAA1@FLA1:H#IA1:H$I%TD%'("

DATE1 = the date the loan commences.

DATE2 = the date the loan ends.

Yield of a Discounted (or Premium) Mortgage

The annual yield of a mortgage bought at a discount or premium can be

calculated given the original mortgage amount (PV), interest rate (I%YR),

periodic payment (PMT), balloon payment amount (if any) (FV), and the

price paid for the mortgage (new PV).

Remember the cash-flow sign convention: money paid out is negative,

money received is positive.

Example: Discounted Mortgage. An investor wishes to purchase a

$100,000 mortgage taken out at 9% for 20 years. Since the mortgage

was issued, 42 monthly payments have been made. The loan is to be

paid in full (a balloon payment) at the end of its fifth year. What is the

yield if the purchase price of the mortgage is $79,000?

1. Since the payment amount (PMT) is not given, calculate it first. To

do this, first assume 20 years’ amortization on the original mortgage

with no balloon payment (so N = 20 × 12, FV = 0, PV =－100,000,

and I%YR = 9).

2. Since the balloon amount is not given, calculate it (FV) next. Use PMT

from step 1, but change N to 5 years (N = 5 × 12).

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3. Finally enter current values for N (less number of payment periods

already passed, or 5 × 12－42) and PV (proposed purchase price,

$79,000); then calculate I%YR for the annual yield.

Step 1: Calculate PMT. Make sure FV = 0.

Keys: Display: Description:

" ]

#$ 5?@2 H<A 0EAH"

Selects menu; sets 12

payments per year and

End mode.

20 @ T <8$+(&((" Figures and stores total

number of payments for a

full 20-year loan with

monthly payments.

9 U

100000 &

5O8/#((K(((&(("

Stores interest rate and

amount of original loan.

(Money paid out is

negative.)

0 X GO8(&((" Sets FV to zero.

W 50:8*,,&-%" Calculates monthly

payment received.

Step 2: Enter the new value for N given a balloon in 5 years, then find

FV, the amount of the balloon.

Keys: Display: Description:

5 @ T <8'(&((" Stores number of

payments for 5 years.

X GO8**K-(-&(." Calculates balloon due in

5 years.

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Step 3: Enter actual, current values for N and PV; then find new I%YR

for discounted mortgage with balloon.

Keys: Display: Description:

R T

- 42 T

<8#*&(("

Stores number of

payments remaining in

5-year loan.

79000 &

5O8/-,K((("

Stores proposed,

discounted purchase price

(new present value).

U ;6@28$(&-$" Calculates percent annual

yield.

Annual Percentage Rate for a Loan with Fees

See appendix F for RPN keystrokes for the next two examples.

The annual percentage rate, APR, incorporates fees usually charged

when a mortgage is issued, which effectively raises the interest rate. The

actual amount received (the PV) by the borrower is reduced, while the

periodic payments remain the same. The APR can be calculated given

the term of the mortgage (N periods), the annual interest rate (I%YR), the

mortgage amount (new PV), and the basis of the fee charged (how the

fee is calculated).

Remember the cash-flow sign convention: money paid out is negative,

money received is positive.

Example: APR for a Loan with Fees. A borrower is charged two points

for the issuance of a mortgage. (One point is equal to 1% of the

mortgage amount.) If the mortgage amount is $60,000 for 30 years

and the interest rate is 11½% annually with monthly payments, what

APR is the borrower paying?

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1. Since the payment amount is not given, calculate it (PMT) first. Use the

given mortgage amount (PV = $60,000) and interest rate (I%YR =

111/2%).

2. To find the APR (the new I%YR), use the PMT calculated in step 1 and

adjust the mortgage amount to reflect the points paid (PV = $60,000

－ 2%). All other values remain the same (term is 30 years; no future

value).

Keys: Display: Description:

]

#$ 5?@2 H<A 0EAH"

If necessary, sets 12

payments per year and

End mode.

30 @ T <8%'(&((" Figures and stores number

of payments.

11.5 U

60000 V

5O8'(K(((&(("

Stores interest rate and

amount of loan.

0 X GO8(&((" No balloon payment, so

future value is zero.

W 50:8/.,+&#-" Borrower’s monthly

payment.

R V

- 2 %

5O8.*K*((&(("

Stores actual amount of

money received by

borrower into PV.

U ;6@28##&-'" Calculates APR.

Example: Loan from the Lender’s Point of View. A $1,000,000,

10-year, 12% (annual interest) interest-only loan has an origination fee

of 3 points. What is the yield to the lender? Assume that monthly

payments of interest are made. (Before figuring the yield, you must

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calculate the monthly PMT = (loan x 12%) ÷ 12 mos.) When calculating

the I%YR, the FV (a balloon payment) is the entire loan amount, or

$1,000,000, while the PV is the loan amount minus the points.

Keys: Display: Description:

" ]

@c e

#$ 5?@2 H<A 0EAH"

If necessary, sets 12

payments per year and

End mode.

10 @ T <8#$(&((" Stores total number of

payments.

1000000 *

12 %/

#$(K(((&((D"

Calculates annual interest

on $1,000,000 ...

12 W 50:8#(K(((&((" ...and calculates, then

stores monthly payment.

1000000

GO8#K(((K(((&(("

Stores entire loan amount

as balloon payment.

- 3 %=

& V

5O8/,-(K(((&(("

Calculates, then stores

amount borrowed (total —

points).

U ;6@28#$&.%" Calculates APR—the yield

to lender.

Loan with an Odd (Partial) First Period

The TVM menu deals with financial transactions in which each payment

period is the same length. However, situations exist in which the first

payment period is not the same length as the remaining periods. This

first period is sometimes called an odd or partial first period.

The following Solver equation calculates N, I%, PV, PMT, or FV for

transactions involving an odd first period, using simple interest for the

odd period. The formula is valid for 0 to 59 days from inception to

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first payment, and a 30-day month is assumed.*

A Solver Equation for Odd-Period Calculations:

EAAI 5OBL;6D#((BG5LA1@FD%(T)#T8/;GLA1@FZ%(I"

L#);6D#((TB50:I50:TB4F5OL;6I<T/GOBF55OL;6I<T"

(For the Z character, press 2 . ´.)

PV = the loan amount.

I% = the periodic interest rate.

DAYS = the actual number of days until the first payment is made.

PMT = the periodic payment.

N = the total number of payment periods.

FV = the balloon payment. A balloon payment occurs at the end of the

last (Nth) period and is in addition to any periodic payment.

The following examples assume that you have entered the equation

named ODD, above, into the Solver. For instructions on entering Solver

equations, see “Solving Your Own Equations,” on page 29.

Example: Loan with an Odd First Period. A 36-month loan for $4,500

has an annual interest rate of 15%. If the first payment is made in 46

days, what is the monthly payment amount?

Select equation ODD in the Solver.

Keys: Display: Description:

E !"Creates menu.

36 T <8%'&((" 36 payment periods.

4500 V 5O8+K.((&((" Stores loan amount.

15 / 12 "Stores periodic, monthly

* You do not need to specify Begin or End mode. If the number of days until the

first payment is less than 30, Begin mode is assumed. If the number of days

until the first payment is between 30 and 59, inclusive, End mode is assumed.

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u ;68#&$." interest rate.

46 ¬ A1@F8+'&((" Stores days until first

payment.

0 X GO8(&((" No balloon payment.

W 50:8/#.-&(%" Calculates payment.

Example: Loan with an Odd First Period Plus Balloon. A $10,000

loan has 24 monthly payments of $400, plus a balloon payment of

$3,000 at the end of the 24th month. If the payments begin in 8 days,

what annual interest rate is being charged?

Select equation ODD.

Keys: Display: Description:

E "Creates menu.

10000 V

24 T

5O8#(K(((&(("

<8$+&(("

Stores known values.

400 & W 50:8/+((&(("

3000 &

X 8 ¬

GO8/%K(((&(("

A1@F8*&(("

u ;68#&'+" Calculates periodic

(monthly) interest rate.

* 12 = #,&'-" Annual interest rate.

Canadian Mortgages

In Canadian mortgages, the compounding and payment periods are not

the same. Interest is compounded semi-annually while payments are

made monthly. To use the TVM menu in the HP 17bII+, you need to

calculate a Canadian mortgage factor to store as I%YR.

1. Set End mode and store 12 Y.

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2. Store 0 W, 6 T, and 200 V.

3. Add 200 to the annual interest rate, make the number negative, and

store it in X.

4. Press U to calculate the Canadian mortgage factor.

5. Continue the problem by supplying the other mortgage values and

solving for the unknown item. Do not change I%YR from step 4.

Example: Canadian Mortgage. What is the monthly payment required

to fully amortize a 30-year, $30,000 Canadian mortgage if the interest

rate is 12%?

Keys: Display: Description:

" ]

. @c

#$ 5?@2 H<A 0EAH"

Displays TVM menu; sets

12 payments per year

with End mode.

0 W 50:8(&(("

6 T <8'&(("

200 V 5O8$((&(("

+ 12 = &

GO8/$#$&(("

U ;6@28##&-#" Calculates I%YR for

Canadian mortgage

factor.

30 @ T <8%'(&((" Stores other values.

30000 V 5O8%(K(((&(("

0 X GO8(&(("

W 50:8/%(#&,$" Monthly payment.

A Solver Equation for Canadian Mortgages:

71<I 5O8/50:B4F5OLLL#);6@2D$((T\L#D'T/#TB#((I<T"

/GOBF55OLLL#);6@2D$((T\L#D'T/#TB#((I<T"

14: Additional Examples 199

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(For the \ operator press @u.)

PV = loan amount, or present value.

PMT = monthly payment amount.

I%YR = annual (Canadian) interest rate as a percent.

N = total number of payment periods for the life of the loan.

FV = remaining balance, or future value.

For instructions on entering Solver equations, see “Solving Your Own

Equations,” on page 29.

Advance Payments (Leasing)

Occasionally payments are made in advance, such as in leasing.

Leasing agreements sometimes call for the extra payments to be made

when the transaction is closed. A residual value (salvage value) can also

exist at the end of the normal term.

The following equation calculates the monthly payment and the annual

yield when one or more payments are made in advance. It can be

modified to accommodate periods other than monthly by changing the

number 12 to the appropriate number of payment periods per year.

Remember the cash-flow sign convention: money paid out is negative,

money received is positive.

A Solver Equation for Advance Payments:

1AOI 50:8L/5O/GOBLF55OL;6@2D#$I<TTTD"

L4F5OL;6@2D#$I</P1AOT)P1AOT

(For the P character press 2 . µ.)

PMT = the monthly payment amount.

PV = the value of the equipment.

FV = the residual value.

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I%YR = the annual interest rate as a percent.

N = the total number of payments.

#ADV = the number of advance payments.

The following example assumes that you have entered the equation ADV,

above, into the Solver. For instructions on entering Solver equations, see

“Solving Your Own Equations,” on page 29.

Example: Leasing with Advance Payments. Equipment worth $750 is

leased to you for 12 months. The equipment is assumed to have no

salvage value at the end of the lease. You agree to make three

payments at the time of closing. What is the monthly payment if the

annual interest rate is 10%?

Select the ADV equation in the Solver.

Keys: Display: Description:

E !"Creates menu.

750 V

12 T

0 X

3 "

P1AO"

10 U

;6@28#(&(("

Stores known values.

W 50:8/'+&+." Calculates payment.

Savings

Value of a Fund with Regular Withdrawals

Example: A Fund with Regular Withdrawals. What are the balances

after 1, 10, and 20 years of a fund that starts at $750,000, has

$20,000 withdrawn at the beginning of each quarter, and earns 10%

annual interest compounded monthly?

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1. Because the compounding periods and the withdrawal periods are

not coincident, you must first convert the nominal interest rate to one in

terms of the withdrawal periods. You can do this using the ICNV

menu, as explained on page 87, “Compounding Periods Different

from Payment Periods.”

2. The rest of the calculation is a straightforward TVM problem.

Remember that money deposited is paid out and therefore negative;

money withdrawn is received and therefore positive.

Step 1: Find the adjusted nominal interest rate.

Keys: Display: Description:

" h !

i !

7E05E4<A;<= 5"

:;0HF?@2"

Displays periodic

interest-rate conversion

menu.

12 1 58#$&((" Stores number of

compounding periods.

10 j <E068#(&((" Stores nominal interest

rate.

k HGG68#(&+-" Calculates effective

interest rate.

4 1 58+&((" Stores number of

withdrawal periods.

j <E068#(&(*" Calculates adjusted

nominal interest rate.

Step 2: Calculate the future values.

Keys: Display: Description:

e e

]

"Switches to TVM menu.

202 14: Additional Examples

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< #(&(*" Clears message to show

NOM% value still in

calculator line.

s U ;6@28#(&(*" Stores adjusted nominal

interest rate in I%YR.

4 Y

Z e

+ 5?@2 JH=;< 0EAH"

Sets 4 payments

(withdrawals) per year

and

Begin mode.

750000 &

5O8/-.(K(((&(("

Stores present (initial)

value of fund.

20000 W 50:8$(K(((&((" Stores withdrawal

amount.

4 T <8+&((" Stores number of

withdrawals in 1 year.

X GO8-+%K%'+&%#" Value of fund at end of

year 1.

40 T <8+(&((" Stores number of

withdrawals over 10

years.

X GO8'+#K*$+&+#" Calculates value of fund at

end of year 10.

20 @ T <8*(&((" Stores number of

withdrawals after 20

years.

X GO8%+*K,**&'(" Calculates value of fund

at end of year 20.

Deposits Needed for a Child’s College Account

See appendix F for RPN keystrokes for this example.

14: Additional Examples 203

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Suppose you want to start saving now to accommodate a future series of

cash outflows. An example of this is saving money for college. To

determine how much you need to save each period, you must know

when you’ll need the money, how much you’ll need, and at what interest

rate you can invest your deposits.

Use a CFLO list to calculate the net uniform series (NUS) of the future

withdrawals:

1. Store zero for all cash flows except the withdrawals. For those cash

flows, store the amounts you will need to withdraw (since this is cash

received, these cash flows will be positive).

2. Store the periodic interest rate in I% and calculate NUS. The NUS

equals the amount of the monthly deposit you will need to make.

You can also calculate the equivalent present value of all the monthly

deposits combined by calculating the net present value, NPV.

Example: Savings for College. Your daughter will be going to college

in 12 years and you are starting a fund for her education. She will need

$15,000 at the beginning of each year for four years. The fund earns

9% annually, compounded monthly, and you plan to make monthly

deposits, starting at the end of the current month. How much should you

deposit each month to meet her educational expenses?

The cash-flow diagram looks like this:

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$0 $0

$0 $0 $0

144

$0 $0

156 168 180

$0 $0 $0

$15,000

Figure 14-1. Flow of Withdrawals

132 178 179 180

9.00

Figure 14-2. Flow of Deposits

Keys: Display: Description:

"Displays current cash-flow

list and CFLO

menu keys.

@cW

p s

G9ECL(T8U"

Clears current list or gets a

new one.

14: Additional Examples 205

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Step 1: Set up a CFLO list.

0 I G9ECL#T8U" Sets initial cash flow,

FLOW(0), to zero.

0 I P:;0HFL#T8#" Stores zero in FLOW(1)

and prompts for the

number of times it occurs.

12 * 12 - 1

G9ECL$T8U"

Stores 143 (for 11 years,

11 months) in #TIMES(1)

for FLOW(1).

15000 I P:;0HFL$T8#" Stores amount of first

withdrawal, at end of

12th year.

I G9ECL%T8U"

0 I P:;0HFL%T8#" Stores cash flows of

zero...

11 I G9ECL+T8U" ...for the next 11 months.

15000 I

G9ECL.T8U"

Stores second withdrawal,

for sophomore year.

0 I

11 I

G9ECL'T8U"

Stores cash flows of zero

for the next 11 months.

15000 I

G9ECL-T8U"

Stores third withdrawal,

for junior year.

0 I

11 I

G9ECL*T8U"

Stores cash flows of zero

for the next 11 months.

15000 I

G9ECL,T8U"

Stores fourth withdrawal,

for senior year.

e E <5OK <4FK <GO"

<HHA ;6"

Done entering cash flows;

gets CALC menu.

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Step 2: Calculate NUS for the monthly deposit.

Keys: Display: Description:

9 / 12

;68(&-."

Figures the periodic

(monthly) interest rate and

stores it in I%.

w <4F8#*$&%(" Amount of monthly deposit

needed to meet

planned withdrawals.

v <5O8#-K,-%&+*" Calculates the net present

value of the monthly

deposits, which is the

same as the NPV of the

four future withdrawals.

Value of a Tax-Free Account

See appendix F for RPN keystrokes for this example.

You can use the TVM menu to calculate the future value of a tax-free or

tax-deferred account, such as an IRA or Keogh account. Remember that

for calculations with cash flows, money paid out is negative and money

received is positive. (Current tax law and your current income will

determine whether just interest or also principal are tax-free, and for

how long. You can solve for either case.)

N = the number of payments until retirement.

I%YR = the annual dividend rate.

PV = the present value of the retirement account.

PMT = the amount of your deposit. (It must be constant for the duration

of the account.)

FV = the future value of the retirement account.

The purchasing power of that future value depends on the inflation rate

and the duration of the account.

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Example: Tax-Free Account. Consider opening an IRA account with a

dividend rate of 8.175%. 1) If you invest $2,000 at the beginning of

each year for 35 years, how much will you have at retirement? 2) How

much will you have paid into the IRA? 3) How much interest will you

have earned? 4) If your post-retirement tax rate is 15%, what is the

after-tax future value of the account? Assume only the interest will be

taxed. (Assume the principal was taxed before deposit.) 5) What is the

purchasing power of that amount, in today’s dollars, assuming an 8%

annual inflation rate?

Keys: Display: Description:

" ]

1 Y

Z e

# 5?@2 JH=;< 0EAH"

Sets 1 payment per year

and Begin mode.

35 T <8%.&((" Stores number of payment

periods until retirement (1

× 35).

8.175 U ;6@28*&#*" Stores dividend rate.

0 V 5O8(&((" Present value of account

(before first payment).

2000 &

50:8/$K(((&(("

Annual payment

(deposit).

X GO8%*-K'+(&+." Calculates amount in

account at retirement.

R W

* R

T =

/-(K(((&(("

Calculates total amount

paid into IRA by

retirement.

+ R

X =

%#-K'+(&+."

Calculates interest you

will earn.

208 14: Additional Examples

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* 15 % = +-K'+'&(-" Taxes at 15% of interest.

& + R

X =

%%,K,,+&%,"

Subtracts taxes from total

FV to calculate after-tax

FV.

X GO8%%,K,,+&%," Stores after-tax future

value in FV.

8 U

0 W

5O8/$$K,,.&%'"

Calculates present-value

purchasing power of the

above after-tax FV at 8%

inflation rate.

Value of a Taxable Retirement Account

See appendix F for RPN keystrokes for this example.

This problem uses the TVM menu to calculate the future value of a

taxable retirement account that receives regular, annual payments

beginning today (Begin mode). The annual tax on the interest is paid out

of the account. (Assume the deposits have been taxed already.)

N = the number of years until retirement.

I%YR = the annual interest rate diminished by the tax rate:

interest rate × (1－tax rate).

PV = the current amount in the retirement account.

PMT = the amount of the annual payment.

FV = the future value of the retirement account.

Example: Taxable Retirement Account. If you invest $3,000 each year

for 35 years, with dividends taxed as ordinary income, how much will

you have in the account at retirement? Assume an annual dividend rate

of 8.175% and a tax rate of 28%, and that payments begin today.

What will be the purchasing power of that amount in today’s dollars,

assuming 8% annual inflation?

14: Additional Examples 209

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Keys: Display: Description:

" ] "Displays TVM menu.

. 1 Y

Z e

# 5?@2 JH=;< 0EAH"

Sets 1 payment per year

and Begin mode.

35 T <8%.&((" Stores years until

retirement.

8.175 - 28 %

*&#*/$&$,"

;6@28.&*,"

Calculates and stores

interest rate diminished by

tax rate.

0 V 5O8(&((" Stores no present value.

3000 & W 50:8/%K(((&((" Stores annual payment.

X GO8%+.K.(.&'#" Calculates future value.

8 U

0 W

5O8/$%K%'*&##"

Calculates present-value

purchasing power of the

above FV at 8%

inflation.

Modified Internal Rate of Return

When there is more than one sign change (positive to negative or

negative to positive) in a series of cash flows, there is a potential for

more than one IRR%. For example, the cash-flow sequence in the

following example has three sign changes and hence up to three

potential internal rates of return. (This particular example has three

positive real answers: 1.86, 14.35, and 29.02% monthly.)

The Modified Internal Rate of Return (MIRR) procedure is an alternative

that can be used when your cash-flow situation has multiple sign

changes. The procedure eliminates the sign change problem by utilizing

reinvestment and borrowing rates that you specify. Negative cash flows

are discounted at a safe rate that reflects the return on an investment in

210 14: Additional Examples

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a liquid account. The figure generally used is a short-term security (T-bill)

or bank passbook rate. Positive cash flows are reinvested at a

reinvestment rate that reflects the return on an investment of comparable

risk. An average return rate on recent market investments might be used.

1. In the CFLO menu, calculate the present value of the negative cash

flows (NPV) at the safe rate and store the result in register 0. Enter

zero for any cash flow that is positive.

2. Calculate the future value of the positive cash flows (NFV) at the

reinvestment rate and store the result in register 1. Enter zero for any

cash flow that is negative.

3. In the TVM menu, store the total number of periods in N, the NPV

result in PV, and the NFV result in FV.

4. Press U to calculate the periodic interest rate. This is the

modified internal rate of return, MIRR.

Example: Modified IRR. An investor has an investment opportunity with

the following cash flows:

Group

(FLOW no.)

No. of Months

(#TIMES) Cash Flow, $

－180,000

100,000

－100,000

200,000

Calculate the MIRR using a safe rate of 8% and a reinvestment (risk) rate

of 13%.

Keys: Display: Description:

" r "Displays current cash-flow

list.

@cW "Clears current list or gets a

14: Additional Examples 211

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p s

G9ECL(T8U"

new one.

180000 &

G9ECL#T8U"

Stores initial cash flow,

FLOW(0).

0 I P:;0HFL#T8#" Stores FLOW(1) as zero

since the flow amount is

positive.

5 I G9ECL$T8U" Stores 5 for #TIMES(1).

100000 &

P:;0HFL$T8#"

Stores FLOW(2).

5 I G9ECL%T8U" Stores FLOW(2) 5 times.

You can skip FLOW(3)

and FLOW(4) because

they are equal to zero for

this part.

e E <5OK <4FK <GO"

<HHA ;6"

8 / 12

;68(&'-"

Stores monthly safe

interest rate.

v <5O8/'.+K#%'&*#" Calculates NPV of

negative cash flows.

s 0 <5O8/'.+K#%'&*#" Stores NPV in register 0.

e G9ECL%T8U" Returns to CFLO menu.

@cW "G9ECL(T8U" Clears list.

0 I G9ECL#T8U" Stores zero as FLOW(0).

(Skip negative flows; store

positive flows.)

100000 I

5 I

G9ECL$T8U"

Stores FLOW(1) 5 times.

0 I "Stores zero for FLOW(2),

212 14: Additional Examples

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5 I G9ECL%T8U" 5 times.

0 I

9 I

G9ECL+T8U"

Stores zero for FLOW(3),

9 times.

200000 I

G9ECL.T8U"

Stores FLOW(4), 1 time.

e E " <5OK <4FK <GO"

<HHA ;6"

13 / 12

;68#&(*"

Stores monthly

reinvestment rate.

x " <GO8*((K.*$&-." Calculates NFV of positive

cash flows.

s 1 <GO8*((K.*$&-." Stores NFV in register 1.

@A "

] .

@c e

#$ 5?@2 H<A 0EAH"

Switches to TVM menu;

sets 12 periods per year

with End mode, if

necessary.

20 T <8$(&((" Stores total number of

investment periods.

R 0 V 5O8/'.+K#%'&*#" Recalls present value of

negative cash flows and

stores in PV.

R 1 X GO8*((K.*$&-." Recalls future value of

positive cash flows and

stores in FV.

0 W 50:8(&((" Stores zero in PMT (no

payments).

U ;6@28#$&#*" Calculates annual MIRR.

14: Additional Examples 213

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Price of an Insurance Policy

The price of an insurance policy, other than term life insurance, is rarely

apparent at first glance. The price should include not only the premium

payments, but also the interest that could have been earned on the cash

value or savings portion of the policy.

The following equation calculates the price per $1,000 of protection for

one policy year and the interest rate earned on the savings portion of

the policy.

To calculate the price, assume some value for interest―for example, the

interest rate you could earn on a one-year savings certificate after tax.

Similarly, to calculate interest, assume a price per $1,000 per year for

alternative insurance; for example, a low-cost term policy of the

one-year renewable type.

Even complex policies like minimum-deposit plans can be analyzed with

this procedure. Use policy surrender values for cash values and the

actual (after-tax) amounts for payments (premiums) and dividends.

A Solver Equation for Insurance Price:

;<F8LL52H0)9O19TBL#);6D#((T/O19/A;OTD"

L&((#BLG17H/O19TT"

INS = the price per $1,000 of protection in one policy year.

PREM = the annual premium amount.

LVAL = the value of the policy at the end of last year.

I% = the rate of return, as a percent, on a savings account.

VAL = the value of the policy at the end of the current year.

DIV = the dollar value of the dividend for one year.

FACE = the face value of the policy for one year.

The following example assumes that you have entered the above

equation into the Solver. For instructions on entering Solver equations,

see “Solving Your Own Equations,” on page 30.

214 14: Additional Examples

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Example: Insurance Policy. You are evaluating your $50,000

insurance policy. The premium of $1,010 is due at the beginning of the

year, and a dividend of $165 is received at the end of the policy year.

The cash value of the policy is $3,302 at the beginning of the year; it

will grow to $4,104 by the end of the year. You can earn 6% on a

savings account. What is the annual price per $1,000 protection?

Select the correct equation in the Solver.

Keys: Display: Description:

E "Creates menu.

1010 "

52H0" 52H08#K(#(&((" Stores annual premium.

3302 "

9O19" 9O198%K%($&((" Stores value of policy at

end of last year.

6 u ;68'&((" Stores interest rate you

could get elsewhere.

4104 "

O19" O198+K#(+&((" Stores value of policy at

end of this year.

)

165 "

A;O"

A;O8#'.&(("

Stores annual dividend.

50000 "

G17H"

G17H8.(K(((&((" Stores face value of

policy.

) "

;<F" ;<F8'&.-" Your protection cost

$6.57 per $1,000 face

(protection) value.

Insurance protection could be purchased for $3 per $1,000 face value.

Calculate the rate of return on your savings.

Keys: Display: Description:

3 "

;<F" ;<F8%&((" Stores price of alternate

insurance.

u ;68$&$(" Calculates rate of return.

14: Additional Examples 215

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Reference: Joseph M. Belth, Life Insurance

―

A Consumer’s Handbook,

Indiana University Press, 1973, p. 234.

Bonds

Example: Yield to Maturity and Yield to Call. On March 16, 2003

you consider the purchase of a $1,000 bond that was issued on

January 1, 2001. It has a 10.5% semiannual coupon using a 30/360

calendar, and matures on January 1, 2031. The bond is callable on

January 1, 2006 at 110 (that is, $1,100). The bond is now selling at

115.174 (that is, $1,151.74). Determine both the yield to maturity and

the yield to call for this bond.

First, calculate the yield to maturity:

Keys: Display: Description:

" y !

"Displays BOND menu.

z •

ƒ e

%(?%'( FH0;1<<419"

Sets semiannual bond

on 30/360 calendar.

@c %(?%'( FH0;1<<419" Clears variables; sets

CALL to 100.

3.162003{ FH::8"

(%?#'?$((% F4<"

Stores today as

purchase date.

1.012031| 01:8(#?(#?$(%# CHA" Stores maturity date.

10.5 } 75<68#(&.(" Stores coupon rate.

)

115.174 *

52;7H8##.&#-"

Stores price. Displays

only two decimal

places, but stores all

three.

• " @9A68,&((" Calculates yield to

maturity.

216 14: Additional Examples

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Second, calculate the yield to call:

Keys: Display: Description:

) @9A68,&((" Returns to first BOND

menu.

1.012006

01:8(#?(#?$((' F4<"

Changes maturity date

to the call date.

110 ~ 71998##(&((" Stores call value.

) • @9A68-&'%" Calculates a yield to

call.

Discounted Notes

A note is a written agreement to pay to the buyer of the note a sum of

money plus interest. Notes do not have periodic coupons, since all

interest is paid at maturity. A discounted note is a note that is purchased

below its face value. The following equations find the price or yield of a

discounted note. The calendar basis is actual/360.

Solver Equations for Discounted Notes: To find the price given the

discount rate:

<E:HI52;7H82O/LA;F7B2OBAA1@FLFH::I01:I#TD%'(((T"

To find the yield given the price (or to find the price given the yield):

<E:HI@;H9A8L2O/52;7HTD52;7HB%'(((D"

AA1@FLFH::I01:I#T"

PRICE = the purchase price per $100 face value.

YIELD = the yield as an annual percentage.

RV = the redemption value per $100.

DISC = the discount rate as a percent.

SETT = the settlement date (in current date format).

MAT = the maturity date (in current date format).

14: Additional Examples 217

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The following example assumes that you have entered the NOTE

equations into the Solver. For instructions on entering Solver equations,

see “Solving Your Own Equations,” on page 30.

Example:Price and Yield of a Discounted Note. What are the price

and yield of the following U.S. Treasury Bill: settlement date October 14,

2003; maturity date March 17, 2004; discount rate 8.7%? (Assume

month/day/year format.)

Select the NOTE:PRICE equation in the Solver.

Keys: Display: Description:

E "Creates menu.

10.142003

{

FH::8#(&#+"

Stores known values.

3.172004

8.7 "

A;F7"

100 "

2O"

01:8%&#-"

A;F78*&-("

2O8#((&(("

* 52;7H8,'&$." Calculates price.

e] E <E:HI@;H9A8"

L2O/52;7HT>"

Displays NOTE:YIELD

equation, then its menu.

@;H9A" @;H9A8,&(+" Calculates yield.

Statistics

Moving Average

Moving averages are often useful in predicting trends in data taken over

a period of time. In moving-average calculations, a specified number of

points is averaged. Each time a new point is acquired, the oldest point

is discarded. Thus, the same number of points is used in each

calculation.

218 14: Additional Examples

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A Solver Equation for Moving Averages:

01O=8^L;I01XL#I91F:/<)#TI91F:I#I;:H0LnameI;TTD"

0;<L<I91F:T"

N = the number of values averaged in each calculation.

LAST = the item number of the most recent value to be averaged.

name = the name of the SUM list whose data will be averaged. When

you create and name the SUM list, make sure its name matches

the name in the Solver equation.

The following example assumes that you have entered the equation

MAVG into the Solver, using VOL for the SUM list’s name. For

instructions on entering Solver equations, see “Solving Your Own

Equations,” on page 30.

Example: A Moving Average in Manufacturing. Calculate a three-

month moving average for the number of units manufactured during the

first half of the year. Manufacturing volumes are:

January February March April May June

4400 5360 2900 3670 4040 3200

Keys: Display: Description:

$ !"Displays SUM menu

and

current list.

@cW

p s

;:H0L#T8U"

Clears current list or

gets

a new one.

4400 I

5360 I

2900 I

3670 I

Enters data.

14: Additional Examples 219

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4040 I

3200 I

;:H0L-T8U"

:E:198$%K.-(&(("

e o

VOL I

;:H0L-T8U"

Names the list VOL.

e &

(use ] and [

if necessary)

"Displays the MAVG

equation. Make sure

name is VOL.

E "Displays menu.

3 T <8%&((" Stores number of

points.

3 e

01O="

01O=8+K$$(&(("

Calculates average for

months 1, 2, and 3.

4 e

01O="

01O=8%K,-'&'-"

Calculates average for

months 2, 3, and 4.

5 e

01O="

01O=8%K.%'&'-"

Calculates average for

months 3, 4, and 5.

6 e

01O="

01O=8%K'%'&'-"

Calculates average for

months 4, 5, and 6.

Chi-Squared ( χ2 ) Statistics

The χ2 statistic is a measure of the goodness of fit between data and an

assumed distribution.* It is used to test whether a set of observed

frequencies differs from a set of expected frequencies sufficiently to

reject the hypothesis under which the expected frequencies were

obtained.

* The statistic can be assumed to be χ2 distributed with n－1 degrees of

freedom if n or some of the Ei values are large.

220 14: Additional Examples

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In other words, it tests whether discrepancies between the observed

frequencies (Oi) and the expected frequencies (Ei) are significant, or

whether they might reasonably result from chance. The equation is:

()

nii

−

=∑

If there is a close agreement between the observed and expected

frequencies, χ2 will be small. If the agreement is poor, χ2 will be large.

Solver Equations for χ2 Calculations:

If the expected value is a constant:

7M;8^L;I#IF;_HFLname1TI#IL;:H0Lname1I;T"

/HX5T\$DHX5T"

If the expected values vary:

7M;$8^L;I#IF;_HFLname1I#IL;:H0Lname1I;T"

/;:H0Lname2I;TT\$D;:H0Lname2I;TT"

(To enter the Σ character, press 2 . ) ¶.)

CHI2 = the final χ2 value for your data.

name1 = the name of the SUM list that contains the observed values.

name2 = the name of the SUM list that contains the expected values.

EXP = the expected value when it is a constant.

When you create and name the SUM list(s), make sure the name(s)

match name1 (and name2, if applicable) in the Solver equation.

To solve the equation, press "7M;$" once or twice (until you see the

message 7197491:;<=>).

The following example assumes that you have entered the CHI equation

into the Solver, using OBS for name1. For instructions on entering Solver

equations, see “Solving Your Own Equations,” on page 30.

Example: Expected Throws of a Die. To determine whether a suspect

die is biased, you toss it 120 times and observe the following results.

(The expected frequency is the same for each number, 120 ÷ 6, or 20.)

14: Additional Examples 221

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Number 1 2 3 4 5 6

Frequency Observed 25 17 15 23 24 16

Keystroke: Display: Description:

$ !"Displays SUM menu and

current list.

@cW

p s

;:H0L#T8U"

Clears current list or gets a

new one.

25 I

17 I

15 I

23 I

24 I

16 I

;:H0L-T8U"

:E:198#$(&(("

Enters observed values.

e o

OBS I

;:H0L-T8U"

Names the list OBS.

e &

(use [ and ]

if necessary )

"Displays the CHI

equation. Make sure

name1

is OBS.

E "Displays menu.

20 I HX58$(&((" Stores expected value.

7M;" "7M;8.&((" Calculates χ2.

The number of degrees of freedom is (n－1)＝5. Consult statistical tables

to find χ2 to a significance level of 0.05 with 5 degrees of freedom. The

table shows that 2

005 5

＝11.07. Since the computed value (5.00) is less

than 11.07, you can conclude that, to a 0.05 significance level (95%

probability), the die is fair.

222 A: Assistance, Batteries, Memory, and Service

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Assistance, Batteries,

Memory, and Service

Obtaining Help in Operating the Calculator

Hewlett-Packard is committed to supporting users of HP calculators. You

can obtain answers to your questions about using the calculator from

our Calculator Support department.

We suggest reading “Answers to Common questions,” below, before

contacting us. Past experience has shown that many of our customers

have similar questions.

Answers to Common Questions

Q: I’m not sure if the calculator is malfunctioning or if I’m doing

something incorrectly. How can I determine if the calculator is operating

properly?

A: Refer to page 232, which describes the diagnostic self-test.

Q: My arithmetic keys don’t work like I expect. I press 12 + 3 = and

get 3.00.

A: You may be in the wrong mode. Press @> 0 to set

Algebraic mode.

Q: My numbers contain commas as decimal points. How do I restore

the periods?

A: Press D F.

A: Assistance, Batteries, Memory, and Service 223

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Q: How do I change the number of decimal places the calculator

displays?

A: The procedure is described in “Decimal Places” on page 34.

Q: How do I clear all or portions of memory?

A: C clears the calculator line. @c clears the data lists or

variables accessible from the current menu. Erasing the entire contents

of memory is covered in “Erasing Continuous Memory” on page 230.

Q: Why am I getting the wrong answer using the TVM menu?

A: Be sure to enter a value for all five TVM variables, even if a value is

zero (as FV is for a loan without a balloon). Clearing the variables

before starting (@c ) accomplishes the same thing. Check the

appropriate payment mode (mortgages and loans are typically End

mode calculations), and specify the number of payments per year

( Y ). Also check that all figures for money paid out are negative

(the cash-flow sign convention).

Q: Can I access the TVM menu functions from the Solver?

A: No, but you can do the same functions by copying the appropriate

financial formulas into the Solver. The formulas are given starting on

page 168.

Q: Can I access the data stored in my CFLO and SUM lists from the

Solver?

A: Yes. See “Accessing CFLO and SUM Lists from the Solver,” page

177.

Q: How do I indicate multiplication in an equation typed into the

Solver?

A: Use the multiplication key (*). You cannot use the letter · in

the ALPHA menu.

Q: What does an “E” in a number (for example, 2.51E－13) mean?

A: Exponent of ten (for example, 2.51 x 10-13). Refer to “Scientific

Notation” on page 47.

Q: The calculator has displayed the message

;<F4GG;7;H<: 0H0E2@. What should I do?

224 A: Assistance, Batteries, Memory, and Service

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A: Refer to “Managing Calculator Memory” on page 227 for

instructions on how to reclaim memory for your use.

Q: The calculator is operating slowly, and the annunciator is

blinking. Why?

A: The calculator is trace printing. Press @p n e to turn

off tracing.

Q: How can I change the sign of a number in a list without keying in the

number again?

A: Press R I & I .

Q: The beeper is not working.

A: Check the beeper mode by pressing @> -. See also

page 36.

Q: The messages and the menu labels in the display are not in English.

How do I restore the English?

A: Models of the HP 17bII+ sold in many countries outside of the United

States include a menu to select the language for messages and labels.

To select the English language, press @> ! $ .

Power and Batteries

The calculator is power by two 3-volt lithium coin batteries.

When changing batteries, use only fresh button-cell batteries. Both

batteries must be changed at the same time.

Do not use rechargeable batteries.

Low-Power Indications

When the low-battery annunciator ( ) comes on, the calculator

can continue normal operation for several hours. If the calculator is

turned off. Continuous Memory will be preserved for approximately two

weeks. To conserve battery power, printing does not function when the

battery annunciator is on. Printing might halt during a printing operation

A: Assistance, Batteries, Memory, and Service 225

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due to a borderline low-battery condition. The calculator can detect that

there is insufficient power for printing before the battery annunciator

comes on.

If you continue to use the calculator after the battery annunciator comes

on, power can eventually drop to a level at which the calculator stops

powering the display and keyboard. The calculator will require fresh

batteries before it can be turned back on. When you turn the calculator

on after fresh batteries have been installed, the calculator displays

017M;<H 2HFH: if your stored data is intact. If data has been lost, the

calculator displays 0H0E2@ 9EF:. In either case, the clock’s time

might be incorrect.

Installing Batteries

Once the batteries are removed, you must replace the batteries

within 30 seconds to prevent loss of Continuous Memory.

To install batteries:

1. Have two fresh CR2032 batteries at hand. Hold batteries by the

edges. Do not touch the contacts. Wipe each battery with a clean,

lint-free cloth to remove dirt and oil.

2. Make sure the calculator is off. Do not press C again until the

entire procedure for changing batteries is completed. Changing

batteries with the calculator on can erase the contents of

Continuous Memory. If you have set any appointments, make sure

they will not come due while the batteries are out.

3. Turn the calculator over and prize off the battery cover.

226 A: Assistance, Batteries, Memory, and Service

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4. Never remove two old batteries at the same time, in case

memory lost. Remove one of the two batteries once. Insert a new

battery, making sure that the positive sign (+) is facing outward.

Warnin

Do not mutilate, puncture, or dispose of batteries in fire.

The batteries can burst or explode, releasing hazardous

chemicals.

5. Remove and insert the other battery as step 4. Make sure that the

positive sign (+) on each battery is facing outward.

6. Replace the battery compartment cover.

7. Press on.

Now turn the calculator back on. If it does not function, you might have

taken too long to change the batteries or inadvertently turned the

calculator on while the batteries were out. Remove the batteries again

and lightly press a coin against both battery contacts in the calculator

for a few seconds. Put the batteries back in and turn the calculator on.

You should see 0H0E2@ 9EF:.

A: Assistance, Batteries, Memory, and Service 227

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Managing Calculator Memory

The calculator has approximately 30,740 units (or “bytes”) of user

memory available. (This is separate from the system memory that stores

all the unerasable information with which the calculator is manufactured.)

The calculator displays ;<F4GG;7;H<: 0H0E2@ if you attempt an

operation that uses more memory than is currently available. If you see

this message:

1. Complete any calculations in the calculator line (press = or C).

This frees the memory that was being used to store each of the

numbers and operators.

2. To further increase the amount of available memory:

Rename the named SUM and CFLO lists with shorter names (see

page 98), and clear any lists you no longer need (see page 99).

! Shorten or delete any messages with appointments (see page

146).

! Delete any Solver variables or equations you no longer need (see

page 164).

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Resetting the Calculator

If the calculator doesn’t respond to keystrokes or is behaving unusually,

attempt to reset it. Resetting the calculator halts the current calculation,

clears the calculator line, and displays the MAIN menu. Stored data

remains intact except setting those conditions: double-space printing off,

printer tracing off, printer without the ac adapter, and beeper on.

To reset the calculator, hold down C while pressing the third menu

key from the left. Repeat if necessary. The calculator displays

017M;<H 2HFH: to confirm that reset has occurred.

The calculator can reset itself if it is dropped or if power is interrupted.

If the calculator still does not respond to keystrokes, use the following

procedures.

1. Use a thin, pointed object to press the reset hole near of the battery

compartment.

Reset hole

2. The calculator displays the INTL (international) menu. You must specify

a language before proceeding (see page 18 for information about

the setting the language).

3. The display will show 0H0E2@"9EF:. Pressing any key will clear

this message from the display.

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For selecting English language:

! ALG mode

! Month/day/year date format, 12-hour clock

! 2 decimal places, period (.) decimal point

! Double-space printing off, printer tracing off, printer without the ac

adapter

! Beeper on

! APPT default time 00.00.00 12:00A, default time WED 01.01.03

12:00:00A

! Erased Continuous Memory

! U.S Dollars and EURO Dollars currencies and the rate equals 1.0000.

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For selecting the other languages:

! ALG mode

! Day/month/year date format, 24-hour clock

! 2 decimal places, comma (,) decimal point

! Double-space printing off, printer tracing off, printer without the ac

adapter

! Beeper on

! APPT default time 00.00.00 00:00, default time WED 01.01.03

00:00:00

! Erased Continuous Memory

! U.S Dollars and EURO Dollars currencies and the rate equals 1.0000.

Erasing Continuous Memory

Erasing Continuous Memory is a way of freeing a large amount of

memory so that you can use it for other things. In addition, the calculator

is set to certain “default” settings.

! Clears the calculator line and history stack.

! Deletes all Solver equations and their variables, and clears all other

variables in menus.

! Clears all CFLO and SUM lists and their names.

! Clears all appointments.

! Returns U.S Dollars and EURO Dollars currencies and the rate equals

1.0000.

! Sets those conditions:

For English language:

Month/day/year date format, 12-hour clock, 2 decimal places,

period (.) decimal point, double-space printing off, printer tracing off,

printer without the ac adapter, and beeper on.

For the other languages:

Day/month/year date format, 24-hour clock, 2 decimal places,

comma (,) decimal point, double-space printing off, printer tracing off,

printer without the ac adapter, and beeper on.

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! Maintains the selected mode－ALG or RPN.

Erasing Continuous Memory does not affect the current time and date,

date and the selected language.

To erase Continuous Memory, press and hold down C, the leftmost

menu key, and the rightmost menu key. (Press three keys simultaneously).

When the three keys are released, the calculator displays 0H0E2@

9EF:.

Continuous Memory can inadvertently be erased if the calculator is

dropped or if power is interrupted.

Clock Accuracy

The clock is regulated by a quartz crystal accurate to within 1.5 minutes

per month under normal conditions. The accuracy of the clock crystal is

affected by temperature, physical shock, humidity, and aging. Optimum

accuracy is maintained at 25°C (77°F).

Environmental Limits

In order to maintain product reliability, observe the following limits:

! Operating temperature: 0° to 45°C (32° to 113°F).

! Storage temperature: －20° to 65°C (－4° to 149°F).

! Operating and storage humidity: 90% relative humidity at 40°C

(104°F) maximum.

Determining If the Calculator Requires

Service

Use these guidelines to determine if the calculator requires service. If it

does, read “Service” on page 235.

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! If the calculator won’t turn on:

1. Attempt to reset the calculator (see page 228).

2. If the calculator fails to respond after step 1, replace the batteries

(see page 225). If you have just replaced the batteries, see page

227.

If these steps do not help, the calculator requires service.

! If the calculator doesn’t respond to keystrokes:

1. Attempt to reset the calculator (see page 228).

2. If the calculator still fails to respond, attempt to erase Continuous

Memory (see page 230). This will erase all the information you’ve

stored.

If these steps do not help, the calculator requires service.

! If the calculator responds to keystrokes but you suspect that it is

malfunctioning:

1. Do the self-test (described below). If the calculator fails the self test,

it requires service.

2. If the calculator passes the self-test, it is quite likely you’ve made a

mistake in operating the calculator. Try rereading portions of the

manual, and check “Answers to Common Questions” on page

222.

3. Contact the Calculator Support department.

Confirming Calculator Operation:

Self-Test

If the display can be turned on, but it appears that the calculator is not

operating properly, you can do a diagnostic self-test. The self-test runs

continuously, repeating until you halt it.

To run the self-test:

1. Turn the calculator on.

2. If you have the optional infrared printer, turn it on. Certain diagnostic

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information is printed during the test.

3. If possible, return to the MAIN menu (press @A).

4. To start the self-test, hold down C while you press the fifth menu

key from the left. Once the self-test has begun, do not press any keys

until you are ready to halt the test.

5. During the test, the calculator beeps periodically and displays various

patterns and characters. Watch for one of two messages that are

displayed before the test automatically repeats:

! If the calculator passes the self-test, the calculator displays

E3"#-J;;)

! If the calculator displays G1;9 followed by a five-digit number,

the calculator requires service.

6. To halt the self-test, hold down C while you press the third menu

key from the left. The calculator displays 017M;<H 2HFH:. If you

press any other key instead, the test halts and the calculator displays

a G1;9 message. This results from an incorrect key being pressed,

and does not mean that the calculator requires service.

7. If the calculator failed the self-test, repeat steps 4 through 6 to verify

the results. If you do not have a printer, write down the messages that

are displayed in step 5.

Warranty

HP 17bII+ Financial Calculator; Warranty period: 12 months

1. HP warrants to you, the end-user customer, that HP hardware,

accessories and supplies will be free from defects in materials

and workmanship after the date of purchase, for the period

specified above. If HP receives notice of such defects during the

warranty period, HP will, at its option, either repair or replace

products which prove to be defective. Replacement products may

be either new or like-new.

2. HP warrants to you that HP software will not fail to execute its

programming instructions after the date of purchase, for the

period specified above, due to defects in material and

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workmanship when properly installed and used. If HP receives

notice of such defects during the warranty period, HP will

replace software media which does not execute its programming

instructions due to such defects.

3. HP does not warrant that the operation of HP products will be

uninterrupted or error free. If HP is unable, within a reasonable

time, to repair or replace any product to a condition as

warranted, you will be entitled to a refund of the purchase price

upon prompt return of the product.

4. HP products may contain remanufactured parts equivalent to new

in performance or may have been subject to incidental use.

5. Warranty does not apply to defects resulting from (a) improper

or inadequate maintenance or calibration, (b) software,

interfacing, parts or supplies not supplied by HP, (c)

unauthorized modification or misuse, (d) operation outside of the

published environmental specifications for the product, or (e)

improper site preparation or maintenance.

6. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION

WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY

LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF

MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS

FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION

OF THE EXPRESS WARRANTY SET FORTH ABOVE. Some

countries, states or provinces do not allow limitations on the

duration of an implied warranty, so the above limitation or

exclusion might not apply to you. This warranty gives you

specific legal rights and you might also have other rights that

vary from country to country, state to state, or province to

province.

7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN

THIS WARRANTY STATEMENT ARE YOUR SOLE AND

EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO

EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF

DATA OR FOR DIRECT, SPECIAL, INCIDENTAL,

CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR

OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR

OTHERWISE. Some countries, States or provinces do not allow

the exclusion or limitation of incidental or consequential damages,

so the above limitation or exclusion may not apply to you.

8. The only warranties for HP products and services are set forth in

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the express warranty statements accompanying such products

and services . Nothing herein should be construed as constituting

an additional warranty.HP shall not be liable for technical or

editorial errors or omissions contained herein.

FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW

ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT,

EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE,

RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY

STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO

YOU.

Service

Europe Country : Telephone numbers

Austria +43-1-3602771203

Belgium +32-2-7126219

Denmark +45-8-2332844

Eastern Europe

countries +420-5-41422523

Finland +35-89640009

France +33-1-49939006

Germany +49-69-95307103

Greece +420-5-41422523

Holland +31-2-06545301

Italy +39-0422-303069

Norway +47-63849309

Portugal +351-213-180020

Spain +34-917-820111

Sweden +46-851992065

Switzerland +41-1-4395358 (German)

+41-22-8278780 (French)

+39-0422-303069 (Italian)

Turkey +420-5-41422523

UK +44-207-4580161

Czech Republic +420-5-41422523

South Africa +27-11-541 9573

Luxembourg +32-2-7126219

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Other European

countries +420-5-41422523

Asia Pacific Country : Telephone numbers

Australia +61-3-9841-5211

Singapore +61-3-9841-5211

L.America Country : Telephone numbers

Argentina 0-810-555-5520

Brazil

Sao Paulo 3747-7799; ROTC

0-800-157751

Mexico

Mx City 5258-9922; ROTC

01-800-472-6684

Venezuela 0800-4746-8368

Chile 800-360999

Columbia 9-800-114726

Peru 0-800-10111

Central America

& Caribbean 1-800-711-2884

Guatemala 1-800-999-5105

Puerto Rico 1-877-232-0589

Costa Rica 0-800-011-0524

N.America Country : Telephone numbers

U.S. 1800-HP INVENT

Canada (905)206-4663 or 800-HP INVENT

ROTC = Rest of the country

Regulatory information

This section contains information that shows how the HP 17bII+

Financial calculator complies with regulations in certain regions. Any

modifications to the calculator not expressly approved by

Hewlett-Packard could void the authority to operate the 17bII+ in these

regions.

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USA

This calculator generates, uses, and can radiate radio frequency energy

and may interfere with radio and television reception. The calculator

complies with the limits for a Class B digital device, pursuant to Part 15

of the FCC Rules. These limits are designed to provide reasonable

protection against harmful interference in a residential installation.

However, there is no guarantee that interference will not occur in a

particular installation. In the unlikely event that there is interference to

radio or television reception(which can be determined by turning the

calculator off and on), the user is encouraged to try to correct the

interference by one or more of the following measures:

! Reorient or relocate the receiving antenna.

! Relocate the calculator, with respect to the receiver.

Canada

This Class B digital apparatus complies with Canadian ICES-003.

Cet appareil numerique de la classe B est conforme a la norme

NMB-003 du Canada.

Japan

この装置は、情報処理装置等電波障害自主規制協議会(VCCI)の基準

に基づく第二情報技術装置です。この装置は、家庭環境で使用するこ

とを目的としていますが、この装置がラジオやテレビジョン受信機に

近接して使用されると、受信障害を引き起こすことがあります。

取扱説明書に従って正しい取り扱いをしてください。

Noise Declaration

In the operator position under normal operation (per ISO 7779): LpA <

70dB.

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More About Calculations

IRR% Calculations

The calculator determines IRR% for a set of cash flows using

mathematical formulas that “search” for the answer. The process finds a

solution by estimating an answer and then using that estimate to do

another calculation―in mathematical terms, this is called an iterative

process.

In most cases, the calculator finds the desired answer, since there is

usually only one solution to the calculation. However, calculating IRR%

for certain sets of cash flows is more complex. There may be more than

one mathematical solution to the problem, or there may be no solution.

In these cases, the calculator displays a message to help you interpret

what has happened.

Possible Outcomes of Calculating IRR%

These are the possible outcomes of an IRR% calculation for which you

have not stored a guess.

! Case 1: The calculator displays a positive answer. This is the only

positive answer. However, one or more negative answers may exist.

! Case 2: The calculator finds a negative answer but a single positive

solution also exists. It displays:

;226[( HX;F:FQ 3H@"

;< =4HFFQ VF:EW R;226S"

To see the negative answer, press <. To search for that positive

answer, you must input a guess. (Refer to “Storing a Guess for IRR%”;

below). There might also be additional negative answers.

! Case 3: The calculator displays a negative answer and no message.

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This is the only answer.

! Case 4: The calculator displays the message:

01<@?<E FE94:;E<FQ 3H@

;< =4HFFQ VF:EW R;226S

The calculation is very complex. It might involve more than one

positive or negative answer, or there may be no solution. To continue

the calculation, you must store a guess.

! Case 5: The calculator displays: <E FE94:;E<

There is no answer. This situation might be the result of an error, such

as a mistake in keying in the cash flows. A common mistake is to put

the wrong sign for a cash flow. A valid cash flow series must have at

least one positive and one negative cash flow.

Halting and Restarting the IRR% Calculation

The search for IRR% may take a relatively long time. You can halt the

calculation at any time by pressing any key. The calculator then displays

the current estimate for IRR%. You can resume the calculation by:

! Pressing

s t while the current estimate is displayed in the

calculator line. This continues the calculation from where it left off.

! Storing a guess for IRR%, discussed below.

Storing a Guess for IRR%

To enter a guess, key in an estimate of IRR% and then press s

You can enter a guess for IRR% at these times:

! Before beginning the calculation. This can reduce the time required to

calculate an answer.

! After you’ve halted the calculation.

! After the calculator has halted the calculation due to any of the above

cases. For cases 3 and 5, however, no (other) solutions will be found.

When calculating IRR% using a guess, the calculator displays the current

estimate of IRR% and the calculated value of NPV for each iteration. The

calculation halts when the calculator finds an answer. However, there

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may be additional positive or negative answers, or no true solution at all.

You can continue searching for other solutions by halting the calculation

and entering a different guess.

One way to obtain a good guess for IRR% is to calculate NPV for

various interest rates (I%). Since IRR% is the interest rate at which NPV

equals zero, the best estimate of IRR% is the interest rate that yields the

value for NPV closest to zero.

To find a good estimate for IRR%, key in a guess for IRR% and press

u Then, press v to calculate NPV for that value. Repeat the

calculation of NPV for several values of I%, and look for trends in the

results. Choose as your guess for IRR% a value of I% that produces an

NPV close to zero.

Solver Calculations

As noted in chapter12, the Solver uses two methods to find solutions,

depending on the complexity of the equation: direct and iterative (an

indirect). To use all the calculating power included in the Solver, it

would help to understand, in a general way, how it works.

Direct Solutions

When you start a calculation (by pressing a menu key), the Solver first

tries to find a direct solution by “isolating” the variable you are solving

for (the unknown). Isolating a variable involves rearranging the equation

so that the unknown variable is by itself on the left-hand side of the

equation. For example, suppose you enter the equation:

PROFIT = PRICE

－

COST

If you’ve stored values for PROFIT and PRICE, pressing ) causes

the Solver to internally rearrange the equation algebraically to solve for

COST (COST is the unknown):

COST = PRICE

－

PROFIT

Answers calculated this way are called direct solutions.

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For certain equations, the unknown can be isolated, but an answer

cannot be calculated with the values stored. Then the calculator displays:

FE94:;E< <E: GE4<A

For example, if you enter an equation:

AREA

＝

LxW

and then enter values for AREA and W, the Solver rearranges the

equation to:

＝

AREA÷W

in order to calculate L. However, if you enter the value zero for W, the

Solver cannot find an answer because division by zero is not allowed.

The Solver can isolate the unknown variable if the equation meets these

conditions:

! The unknown variable occurs only once in the equation.*

! The only functions in which the unknown variable appears are ALOG,

DATE, DDAYS (actual calendar only), EXP, EXPM1, IF (in then and else

clauses only), INV, LN, LNP1, LOG, S, SQ, and SQRT.

! The only operators involving the unknown variable are＋,－,x, ÷ , and

^ (power). If you are solving for a variable raised to a positive, even

power (for example, A ^ 2＝4), there may be more than one solution.

However, if the Solver can isolate the variable, it will find one of the

solutions using the positive root. For example, the Solver rearranges A

^ 2 ＝4 to A＝4and calculates the answer＋2.†

! The unknown variable does not appear as an exponent.

* Exceptions: (1) Occurrences of the unknown variable as the argument of the S

function are ignored. (2) The unknown variable can appear twice within an IF

function: once in the then clause and once in the else clause.

† The Solver’s ability to find a solution iteratively can often be enhanced by

rewriting the equation so that the unknown variable does not appear as a

divisor. For example, the Solver may more easily solve for A if the equation 1

÷(A ^ 2–A)＝B is rewritten as (A ^ 2–A) ×B＝1.

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Iterative Solutions

If the Solver is not able to isolate the unknown variable, it cannot

provide a direct solution. In these cases, the Solver searches iteratively

for a solution.*

In its iterative search for a solution, the Solver looks for a value that sets

the left side of the equation equal to the right side. To do this, the Solver

starts with two initial estimates of the answer, which we’ll call estimate

#1 and estimate #2. Using estimate #1, the Solver calculates values for

the left and right side of the equation (LEFT and RIGHT) and calculates

LEFT minus RIGHT (LEFT－RIGHT). Then, the Solver does the same

calculations for estimate #2. If neither estimate produces a value of zero

for LEFT－RIGHT, the Solver analyzes the results and produces two new

estimates that it judges to be closer to the answer. By repeating this

process many times, the Solver narrows in on the answer. During this

search, the calculator displays the two current estimates and the sign of

(LEFT－RIGHT) for each estimate, as shown.

Sign of LEFT－RIGHT for each estimate

Since calculators cannot do calculations with infinite precision (the HP

17bII+ uses 12 digits in its calculations), sometimes the Solver will be

unable to find an estimate where LEFT－RIGHT is exactly zero. However,

the Solver can distinguish between situations where the current estimate

could be a solution, and situations where no solution is found.

* Exceptions: (1) Occurrences of the unknown variable as the argument of the S

function are ignored. (2) The unknown variable can appear twice within an IF

function: once in the then clause and once in the else clause.

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The iterative search for a solution sometimes takes several minutes. (You

can halt the search at any time by pressing any key except @ ) There

are four possible outcomes:

! Case 1: The calculator displays an answer. This is very likely the true

solution for the unknown variable.

There are two situations in which the Solver returns a case 1 answer:

! Case la: LEFT－RIGHT is exactly zero.

! Case lb: LEFT－RIGHT is not zero for either estimate. However,

the Solver has found two estimates that cannot get any closer

together. (Numbers that are as close together as possible are

called neighbors.) Furthermore, LEFT－RIGHT is a positive value

for one estimate and a negative value for the other estimate.

Case 1a:

is exactly 0.

Case 1b:

is not exactly 0.

and are relatively

close to

ether. The two estim-

ates are "nei

hbors".

If you want to know whether LEFT

－

RIGHT is exactly zero, press the

menu key for the unknown variable. If LEFT

－

RIGHT is not equal to

zero, the calculator displays the values of LEFT and RIGHT.

The equation could have more than one iterative solution. If the

answer does not seem reasonable, enter one or two guesses and

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restart the search.

! Case 2: The calculator displays the values of LEFT and RIGHT, which

are unequal. To see the calculator’s result, press < or C. If LEFT

and RIGHT are relatively close to one another in value, the result is

probably a true solution. Otherwise, the result is probably not a true

solution.

If the result seems unreasonable, it could be because the equation has

more than one solution. You might want to enter one or two guesses

and restart the search.

If you want to obtain additional information about the answer, press

and hold down the menu key for the unknown variable until the numbers

in the display stop changing. At this point, the Solver is displaying the

final estimates and the signs of LEFT－RIGHT for each estimate.

This information can be helpful:

! Case 2a: If the signs of LEFT－RIGHT are opposite, and the two

estimates are as close together as two 12-digit numbers can get

(neighbors), the Solver found two estimates that “bracket” an

ideal solution (a solution where LEFT－RIGHT equals zero). If LEFT

and RIGHT are relatively close together, the answer is probably a

solution.

! Case 2b: If the signs of LEFT－RIGHT are opposite, and the two

estimates are not neighbors, be very cautious about accepting the

answer as a solution. If LEFT and RIGHT are relatively close

together, the answer is probably a solution.

! Case 2c: If LEFT－RIGHT for the two estimates have the same sign,

the Solver has halted because it could find no estimates that

further reduced the magnitude of LEFT－RIGHT. Be very cautious

about accepting the answer. If the values of LEFT and RIGHT are

not relatively close to one another, you should reject the answer.

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Case 2a:

have opposite

ns. The two estimates are

"nei

hbors".

Case 2b:

have opposite

ns. The two estimates are

far apart.

Case 2c:

have the same

n..

! Case 3: The calculator displays:

J1A =4HFFHFI"

52HFF V792W :E O;HC"

The Solver is unable to begin its iterative search for a solution using

the current initial estimates (guesses). You might find a solution by

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entering different estimates. The closer you can estimate the answer,

the more likely that the Solver will find a solution.

! Case 4: The calculator displays: FE94:;E< <E: GE4<E

The Solver is unable to find a solution. Check your equation to make

sure you have made no errors in entering it. Also check the value of

each known variable. If your equation and variables are correct, you

might be able to find a solution by entering very good guesses.

Equations Used by Built-in Menus

Actuarial Functions

n＝number of compounding periods.

i%＝periodic interest rate, expressed as a percentage.

Single Payment Present Value Function

(Present value of a single $1.00 payment made after n periods.)

(%: ) 1 100

SPPV i n







－

＝　＋　

Single Payment Future Value Function

(Future value after n periods of a single $1.00 payment.)

(%: ) 1 100

SPFV i n







＝＋

Uniform Series Present Value Function

(Present value of a $1.00 payment that occurs n times.)

1 1 100

(%: ) %

100

USPV i n i







－

－　＋　

＝

Uniform Series Future Value Function

(Future value of a $1.00 payment that occurs n times.)

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1 1

100

( % : ) %

100

USFV i n i







＋

－

＝

Percentage Calculations in Business (BUS)

























－

＝

－

＝

－

＝

% 100

NEW OLD

CHANGE OLD

PART

TOTAL TOTAL

PRICE COST

MARKUP C COST

PRICE COST

MARKUP P PRICE

Time Value of Money (TVM)

S = payment mode factor (0 for End mode; 1 for Begin mode).



++ × × ×





＝

＝＋

I%YR

i% P/YR

0 PV 1 ( % : )

100

iSPMT USPV i n FV SPPV(i% : n)

Amortization

∑INT＝accumulated interest

∑PRIN＝accumulated principal

i＝periodic interest rate

BAL is initially PV rounded to the current display setting.

PMT is initially PMT rounded to the current display setting.

/ 100

IYR

iPYR

＝

For each payment amortized:

248 B: More About Calculations

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INT’ ＝ BAL x i (INT’ is rounded to the current display setting;

INT’ ＝ 0 for period 0 in Begin mode)

INT ＝ INT’ (with sign of PMT )

PRIN ＝ PMT + INT’

BALnew ＝ BALold + PRIN

∑INTnew ＝ ∑INT old + INT

∑PRINnew ＝ ∑PRIN old + PRIN

Interest Rate Conversions

Periodic compounding

% 1 1 100

100

NOM

EFF P





+−×











＝

Continuous compounding

100

% 1 100

NOM

EFF e



−×





＝

Cash-Flow Calculations

j ＝ the group number of the cash flow.

CFj ＝ amount of the cash flow for group j.

nj ＝ #TIMES the cash flow occurs for group j.

k ＝ the group number of the last group of cash flows.

total number of cash flows prior to group j

( x (%: ) (%: ))

jj j

NPV CF CF USPV i n x SPPV i N

≤

∑

1＜j

＝

When NPV = 0, the solution for i% is IRR%.

B: More About Calculations 249

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∑

＝＝

＝

(%: )

( )

NFV NPV SPFV i N where N n

NPV

NUS USPV i N

TOTAL n CF

Bond Calculations

Reference: Lynch, John J., Jr. and Jan H. Mayle, Standard Securities

Calculation Methods, Securities Industry Association, New York, 1986.

A＝accrued days, the number of days from beginning of coupon period

to settlement date.

E＝number of days in coupon period bracketing settlement date. By

convention, E is 180 (or 360) if calendar basis is 30/360.

DSC＝number of days from settlement date to next coupon date. (DSC

＝

－

A).

M＝coupon periods per year ( 1 ＝ annual, 2 ＝ semiannual),

N＝number of coupon periods between settlement and redemption dates.

If N has a fractional part (settlement not on coupon date), then

round it to the next higher whole number.

Y＝annual yield as a decimal fraction, YLD% / 100.

For one or fewer coupon period to redemption:

CPN

CALL ACPN

PRICE DSC Y EM

















+×









＝－

For more than one coupon period to redemption:

250 B: More About Calculations

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−+





















−×



















∑

＝

＋

DSC

CALL

PRICE

CPN

ACPN

The “end-of-month” convention is used to determine coupon dates in the

following exceptional situations. (This affects calculations for YLD%,

PRICE, and ACCRU.)

! If the maturity date falls on the last day of the month, then the coupon

payments will also fall on the last day of the month. For example, a

semiannual bond that matures on September 30 will have coupon

payment dates on March 31 and September 30.

! If the maturity date of a semiannual bond falls on August 29 or 30,

then the February coupon payment dates will fall on the last day of

February (28, or 29 in leap years).

Depreciation Calculations

For the given year, YR#:

−

−×−+

× 

×−





＝

(# 1)

100

( # 1)

( 1)

%/100 ( %/100)

ACRS

ACRS BASIS

BASIS SALV

SL LIFE

BASIS SALV

SOYD LIFE YR

LIFE

BASIS FACT FACT

DB LIFE LIFE

B: More About Calculations 251

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For the last year of depreciation, DB equals the remaining depreciable

value for the prior year.

Sum and Statistics

n＝number of items in the list.

x’＝an element of the sorted list.

for odd n, where 2

( )

for even n, where

( )

( -

TOTAL x MEAN x n

MEDIAN x j

xx n

MEDIAN j

STDEV n

WMN

===

′

′′

Σ−

=−

Σ22

) ()

. () 1

ii i

yx y x

GSD

−

=−

ΣΣ

RANGE ＝ MAX － MIN

Forecasting

Model Transformation Xi Y

LIN

EXP

LOG

PWR

y = B + Mx

y = BeMx

y = B + M ln x

y = BxM

y = B + Mx

In y = ln B + Mx

y = B + M ln x

ln y = ln B + M ln x

ln xi

ln yi

252 B: More About Calculations

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ΣΣ

=Σ − =Σ −

=Σ − −

Let:

2 ( ) 2 ( )

( ) ( )

Then:

SX X X SX Y Y

SXY X X Y Y

= 2

SXY

MSX

B = b for LIN and LOG models, and

B = eb for EXP and PWR models,

where

bYMX

=−

CORR 2 2

SXY

SX SY

=×

Equations Used in Chapter 14

Canadian Mortgages

−−



−+

=− − +











=+ −









1 (1 )

(1 )

where: 1 1

200

PV PMT FV r

CI YR

N = total number of monthly payments

CI%YR = annual interest rate (as a percent)

PV = loan amount

PMT = monthly payment

FV = balloon payment

B: More About Calculations 253

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Odd-Period Calculations

−−



+× =







−+

−+× × × − +





1 (1 )

(1 ) (1 )

DAYS

PV i

iS PMT FV i

Where: PV = loan amount

i = periodic interest rate as a decimal

DAYS = actual number of days until the first payment

PMT = periodic payment amount

N = total number of payments

FV = balloon payment amount

S = 1 if DAYS < 30

S = 0 if DAYS ≥ 30

Advance Payments

( # )

(1 )

1 (1 ) #

NADV

PV FV i

PMT iADV

−

−−

−− +

=

−+ +





where: PMT = payment amount

PV = loan amount

FV = balloon payment amount

i = periodic interest rate (as a decimal)

N = total number of payments

#ADV = number of payments made in advance

Modified Internal Rate of Return

100 1

NFV

MIRR NPV







=−



−







where: n = total number of compounding periods

NFVP = net future value of positive cash flows

NPVN = net present value of negative cash flows

254 C: Menu Maps

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Menu Maps

The following maps show how to display each of the menus. There is a

map for each menu label in the MAIN menu and for each menu found

on the keyboard. The menu labels for variables are enclosed in boxes to

illustrate how they are used:

Variable used to store and calculate values.

Variable used to calculate or display values; cannot be

used to store values.

Variable used to store values; cannot be used to calculate

values.

%CHG

OLD NEW %CH

MU%P

BUS

%TOTL MU%C

COST PRICE M%C

TOTAL PART %T COST PRICE M%P

Figure C-1. BUS Menu

C: Menu Maps 255

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CURR1 C.RCL

CURRX

CURR2 RATE C.STO SELCT

Currencies

Figure C-2. CURRX Menu

256 C: Menu Maps

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FIN

TVM ICNV CFLO

NOM% EFF% P NOM% EFF%

CALC INSR DELET NAME GET #T?

＊

NEW Names of Lists

TOTAL IRR% I% NPV NUS NFV

NI%YRPVPMTFVOTHER

P/YR BEG END AMRT

#P INT PRIN BAL NEXT TABLE

FIRST LAST INCR GO

Figure C-3. FIN Menu

C: Menu Maps 257

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FIN

BOND DEPRC

BASIS SALV LIFE ACRS MORE

YR# DB SOYD SL MORE

TYPE SETT MAT MORE

YLD% PRICE

360 A/A SEMI ANN

Figure C-3 (continued). FIN Menu

258 C: Menu Maps

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SUM

CALC TOTAL

Names of lists

TOTAL MEAN MEDN RANG MORE

SORT FRCST MORE

INSR DELET NAME GET

ALPHA-Edit menu*

ALPHA menu*

MIN MAX

(Select x and

)

MOREx-list

-list CORR M B

MOREMODL W.MN G.SD SIZE

LIN LOG EXP PWR

Figure C-4. SUM Menu

* For the complete menu, see pages 30-31.

C: Menu Maps 259

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TIME

CALC APPT SET

APT1 APT2 ...MORE ...

TIME

M/D 12/24 HELP

MIN

A/PM MSG RPT HELP

A/PM

DATE1 DAYS 360D 365D

Figure C-5. TIME Menu*

* For the complete menu, see pages 30-31.

260 C: Menu Maps

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ALPHA-Edit menu* ALPHA menu*

CALC EDIT NEW

SOLVE

Figure C-6. SOLVE Menu

FIX ALL

DISP

LOG

MATH

LN EXP N! PI

MODES

BEEP PRNT DBL ALG RPN

LIST

PRINTER

STK REGS TIME MSG TRACE

INTL

Figure C-7. DSP, MATH, MODES, and PRINTER Menus

* For the complete menu, see pages 30-31.

D: RPN: Summary 261

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RPN: Summary

About RPN

The RPN appendixes (D, E, and F) are especially for those of you who

want to use or learn RPN―Hewlett-Packard’s original Reverse Polish

Notation for operating calculators. This calculator can use either RPN or

algebraic logic for calculations―you choose which.

HP’s RPN operating logic is based on an unambiguous,

parentheses-free mathematical logic known as “Polish Notation,”

developed by the Polish logician Jan Łukasiewicz (1878－1956).

While conventional algebraic notation places the operators between the

relevant numbers or variables, Łukasiewicz’s notation places them

before the numbers or variables. For optimal efficiency of the stack, we

have modified that notation to specify the operators after the numbers.

Hence the term Reverse Polish Notation, or RPN.

Except for the RPN appendixes, the examples and keystrokes in this

manual are written entirely using Algebraic (ALG) mode.

About RPN on the HP 17bII+

This appendix replaces much of chapter 2, “Arithmetic.” It assumes that

you already understand calculator operation as covered in chapter 1,

“Getting Started.” Only those features unique to RPN mode are

summarized here:

! RPN mode.

! RPN functions.

! RPN arithmetic, including percentages and s and R

arithmetic.

262 D: RPN: Summary

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All other operations－including the Solver－work the same in RPN and

ALG modes. (The Solver uses algebraic logic only.)

For more information about how RPN works, see appendix E, “RPN: The

Stack.” For RPN keystrokes of selected examples from chapter 14, see

appendix F, “RPN: Selected Examples.” Continue reading in chapter 2

to learn about the other functionality of your calculator.

Watch for this symbol in the margin earlier in the manual.

It identifies keystrokes that are shown in ALG mode and

must be performed differently in RPN mode. Appendixes D,

E, and F explain how to use your calculator in RPN mode.

The mode affects only arithmetic calculations－all other

operations, including the Solver, work the same in RPN and ALG

modes.

Setting RPN Mode

The calculator operates in either RPN (Reverse Polish Notation) or ALG

(Algebraic) mode. This mode determines the operating logic used for

arithmetic calculations.

To select RPN mode: Press @> 1.

The calculator responds by displaying 25< 0EAH. This mode remains

until you change it. The display shows the X register from the stack.

To select ALG mode: Press @> 0. The calculator displays

19=HJ21;7 0EAH.

D: RPN: Summary 263

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Where the RPN Functions Are

Function

Name

Definition Key to Use

ENTER Enters and separates one

number from the next.

LASTX Recalls last number in

X-register.

R↓ Rolls down stack contents. ~ (same as ()

R↑ Rolls up stack contents. [ (except in lists)

X < > Y X-register exchanges with

Y-register.

x (same as ))

CHS Changes sign. &

264 D: RPN: Summary

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Using INPUT for ENTER and ▼ for R↓. Except in CFLO and SUM lists,

the I key also performs the E function and the ] key also

performs the ~ function.

! In lists: I stores numbers. Use = to enter numbers into the

stack during arithmetic calculations.

! In lists:

[ and ] move through lists. Use ~ to roll through stack

contents.

Doing Calculations in RPN

Arithmetic Topics Affected by RPN Mode

This discussion of arithmetic using RPN replaces those parts of chapter 2

that are affected by RPN mode. These operations are affected by RPN

mode:

! Two-number arithmetic (+, *, -, /, u).

! The percent function (%).

! The LAST X function (@L). See appendix E.

RPN mode does not affect the MATH menu, recalling and storing

numbers, arithmetic done inside registers, scientific notation, numeric

precision, or the range of numbers available on the calculator, all of

which are covered in chapter 2.

Simple Arithmetic

Here are some examples of simple arithmetic. Notice that

! E separates numbers that you key in.

! The operator (+, -, etc.) completes the calculation.

! One-number functions (such as v) work the same in ALG and RPN

modes.

D: RPN: Summary 265

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To select RPN mode, press @>1.

To Calculate: Press: Display:

12 + 3 12 E 3 + #.&(("

12 – 3 12 E 3 - ,&(("

12 x 3 12 E 3 * %'&(("

12 ÷ 3 12 E 3 / +&(("

122 12

@w #++&(("

12 12

@v %&+'"

1/12 12

@t (&(*"

You do not need to use E before an operator, only between

keyed-in numbers. Key in both numbers (separated by E) before

pressing the operator key.

The Power Function (Exponentiation). The power function uses the

@u keys.

To Calculate: Press: Display:

123 12

E 3 @u #K-$*&(("

121/3 (cube root) 12 E 3 @t @u $&$,"

The Percent Function. The % key calculates percentages without using

the * key. Combined with + or -, it adds or subtracts percentages.

To Calculate: Press: Display:

27% of 200 200 E 27 % .+&(("

200 less 27% 200 E 27 %- #+'&(("

12% greater than 25 25 E 12 %+ $*&(("

Compare these keystrokes in RPN and ALG modes:

266 D: RPN: Summary

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RPN Mode ALG Mode

27% of 200 200 E 27 % 200

* 27 %=

200 less 27% 200 E 27 %- 200

- 27 %=

Calculations with STO and RCL

The store (s) and recall (R) operations work identically in ALG

and RPN modes (see “Storing and Recalling Numbers” and “Doing

Arithmetic Inside Registers and Variables” in chapter 2). The keystrokes

are the same for simple storing and recalling and for doing arithmetic

inside registers and variables.

When doing arithmetic in the display with values from storage registers

and variables, remember to use RPN. Compare these keystrokes in RPN

and ALG modes:

RPN Mode ALG Mode

Store－2 x 3 in

2 &E 3 *s

2 &* 3 =s 5

Find PV－2 " ] R

V 2 -

" ] R

V - 2 =

Find PV less 2% " ] R

V 2 %-

" ] R

V - 2 % =

Find PMT x N " ] R

W R T

" ] R

W *R

T =

Chain Calculations－No Parentheses!

The speed and simplicity of calculating using RPN are apparent during

chain calculations－longer calculations with more than one operation.

The RPN memory stack (refer to appendix E) stores intermediate results

until you need them, then inserts them into the calculation.

D: RPN: Summary 267

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The cube root example and the percentage addition example (previous

topics) are two simple examples of chain calculations.

For another example, calculate

7 x (12 + 3)

Start the calculation inside the parentheses by finding 12 + 3. Notice

that you don’t need to press E to save this intermediate result (15)

before proceeding. Since it is a calculated result, it is saved

automatically－without using parentheses.

Keys: Display: Description:

12 E 3 + #.&((" Intermediate result.

7 * #(.&((" Pressing the function key

produces the answer.

Now study these examples. Note the automatic storage and retrieval of

intermediate results.

To Calculate: Press: Display:

(750 x 12) ÷ 360 750

E 12 * 360 / $.&(("

360 ÷ (750 x 12) 360 E 750 E 12 */

750 E 12 * 360 x/

(&(+"

{(456－75) ÷ 18.5}

x (68 ÷ 1.9)

456 E 75 - 18.5 / 68

E 1.9 /*

-%-&(-"

(3＋4) x (5＋6) 3

E 4 + 5 E 6 + * --&(("

268 E: RPN: The Stack

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RPN: The Stack

This appendix explains how calculations take place in the automatic

memory stack and how this method minimizes keystrokes in complicated

calculations.

What the Stack Is

Automatic storage of intermediate results is the reason that RPN mode

easily processes complicated calculations－without using parentheses.

The key to automatic storage is the automatic RPN memory stack.

The memory stack consists of up to four storage locations, called

registers, which are “stacked” on top of each other. It is a work area for

calculations. These registers－labeled X, Y, Z, and T －store and

manipulate four current numbers. The “oldest” number is the one in the

T-(top) register.

T 0.00 “Oldest” number

Z 0.00

Y 0.00

X 0.00 Displayed (most “recent” number)

The most “recent” number is in the X-register: This is the number you see

in the display.

E: RPN: The Stack 269

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Reviewing the Stack (Roll Down)

The ~ (roll down) function (on the ( key) lets you review the entire

contents of the stack by “rolling” the contents downward, one register at

a time. While in RPN mode you don’t need to press the shift key for ~.

The ] key has the same effect as ~. except in a CFLO or SUM list,

when ] affects the list and not the stack. Likewise, the [ key rolls the

contents of the stack upward, except in lists.

Rolling a Full Stack. Suppose the stack is filled with 1, 2, 3, 4 (press 1

E 2 E 3 E 4). Pressing ~ four times rolls the numbers all

the way around and back to where they started:

T 1 4 3 2 1

Z 2 1 4 3 2

Y 3 2 1 4 3

X 4 ~3 ~2 ~1 ~4

When you press ~, the value in the X-register rotates around into the

T-register. Notice that the contents of the registers are rolled, while the

registers themselves maintain their positions. The calculator displays

only the X-register.

Variable Stack Size. Clearing the stack by pressing @c reduces

the stack to one register (X) with a zero in it. As you enter numbers, the

stack builds up again. The ~ and [ functions roll through as many

registers as currently exist (one, two, three, or four).

Exchanging the X- and Y-Registers in the Stack

Another function that manipulates the stack contents is x(x exchange

y), located on the ) key. It swaps the contents of the X- and Y-registers

without affecting the rest of the stack. Pressing x again restores the

original order of the contents. While in RPN mode you don’t need to

press the shift key for x.

270 E: RPN: The Stack

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The x function is used primarily to swap the order of numbers in a

calculation. For example, an easy way to calculate 9 ÷ (13x8) is to

press 13 E 8 * 9 x/.

Arithmetic－How the Stack Does It

The contents of the stack move up and down automatically as new

numbers enter the X-register (lifting the stack), and as operators combine

two numbers to produce one new number in the X-register (dropping the

stack). See how a full stack drops, lifts, and drops its contents while

calculating

3＋4－9：

a (lost)

T a a a a

Z b a b a

Y 3 b 7 b

4 4 + 7 9 9 - －2

Drop Lift Drop

(a and b represent values already on the stack.)

! Notice that when the stack drops, it replicates the contents of the

T-register and overwrites the X-register.

! When the stack lifts, it pushes the top contents out of the T-register,

and that number is lost. This shows that the stack’s memory is limited

to four numbers for calculations.

! Because of the automatic movement of the stack, you do not need to

clear the display before doing a new calculation.

! Most functions (except E and C) prepare the stack to lift its

contents when the next number enters the X-register.

E: RPN: The Stack 271

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How ENTER Works

You know that E separates two numbers keyed in one after the

other. In terms of the stack, how does it do this? Suppose the stack is

filled with a, b, c, and d. Now enter and add two new numbers:

5＋6：

a (lost) b (lost)

T a b c c c

Z b c d d c

Y c d 5 5 d

X d 5 5 E 5 6 6 + 11

Lift Lift No lift Drop

E replicates the contents of the X-register into the Y-register. The

next number you key in (or recall) writes over (instead of lifting) the copy

of the first number left in the X-register. The effect is simply to separate

two sequentially entered numbers.

Using a Number Twice in a Row. You can use the replicating feature of

E to other advantages. To add a number to itself, key in the number

and press E+.

Filling the Stack with a Constant. The replicating effect of E,

together with the replicating effect (from T into Z) of stack drop, allows

you to fill the stack with a numeric constant for calculations.

Example: Constant, Cumulative Growth. The annual sales of a small

hardware company are projected to double each year for the next 3

years. If the current sales are $84,000, what are the annual sales for

each of the next 3 years?

1. Fill the stack with the growth rate (2 EEE).

2. Key in the current sales in thousands (84).

272 E: RPN: The Stack

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3. Calculate future sales by pressing * for each of the next 3 years.

2 2 2 2 2

E 2 84 84 * 168 * 336 * 672

Sales for the next 3 years are projected to be $168,000; $336,000;

and $672,000.

Clearing Numbers

Clearing One Number. Clearing the X-register puts a zero in it. The

next number you key in (or recall) writes over this zero.

There are two ways to clear the number in the X-register:

! Press

For example, if you wanted to enter 1 and 3 but mistakenly entered 1

and 2, these keystrokes would correct it:

1 1 1 1

1 1 E 1 2 2 < 0 3 3

Clearing the Entire Stack. Pressing @c clears the X-register to

zero and eliminates the Y-, Z-, and T-registers (reducing the size of the

stack to one register). The stack expands again when you enter more

numbers.

E: RPN: The Stack 273

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T a

Z b

Y c

X d @c 0.00

Because of the automatic movement of the stack, it is not necessary to

clear the stack before starting a calculation. Note that if an application

menu is currently displayed, pressing @c also clears the

application’s variables.

The LAST X Register

Retrieving Numbers from LAST X

The LAST X register is a companion to the stack: It stores the number that

had been in the X-register just before the last numeric operation (such as

a * operation). Pressing @L returns this value to the X-register.

This ability to recall the “last x” value has two main uses:

! Correcting errors: retrieving a number that was in the X-register just

before an incorrect calculation.

! Reusing a number in a calculation.

Reusing Numbers

You can use @L to reuse a number (such as a constant) in a

calculation. Remember to enter the constant second, just before

executing the arithmetic operation, so that the constant is the last

number in the X-register, and therefore can be saved and retrieved with

@L.

Example: Calculate 96.74 + 52.39

52.39

274 E: RPN: The Stack

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Keys: Display: Description:

96.74 E ,'&-+"

52.39 + #+,&#%" Intermediate result.

@L .$&%," Retrieves the number

before the + operation,

saved in LAST X.

/ $&*." Final result.

Chain Calculations

The automatic lifting and dropping of the stack’s contents let you retain

intermediate results without storing or reentering them, and without

using parentheses. This is an advantage the RPN stack has over

algebraic calculator logic. Other features of RPN include the following:

! You never work with more than two numbers at a time.

! E separates two numbers keyed in sequentially.

! Pressing an operator key executes that operation immediately.

! Intermediate results appear as they are calculated, so you can check

each step as you go.

! Intermediate results are automatically stored. They reappear

automatically as they are needed for the calculation－the last result

stored is the first to come back out.

! You can calculate in the same order as you would with pencil and

paper－that is, from the innermost parentheses outward:

4 ÷ [14＋(7x3)－2]＝0.12

can be solved as 7 E 3 * 14 + 2 - 4 x/

E: RPN: The Stack 275

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Exercises

Here are some extra problems that you can do to practice using RPN.

Calculate: (14 + 12) x (18 – 12) ÷ (9 – 7)＝78.00

A Solution: 14 E 12 + 18 E 12 -* 9 E 7 -/

Calculate: 232 – (13 x 9) + 1/7＝412.14

A Solution: 23 @w 13 E 9 *- 7 @t +

Calculate: 3

(5.4 0.8) (12.5- 0.7 ) = 0.60×÷

A Solution: 5.4 E .8 * .7 E 3 @u 12.5

x-/@v

5.4 E .8 * 12.5 E .7 E 3 @u-/@v

Calculate: ×÷ ×

××

8.33 (4 - 5.2) [ (8.33- 7.46) 0.32] =4.57

4.3 (3.15-2.75)-(1.71 2.01)

A Solution: 4 E 5.2 - 8.33 *@L 7.46 - .32 */

3.15 E 2.75 - 4.3 * 1.71 E 2.01 *-/@v

276 F: RPN: Selected Examples

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RPN: Selected Examples

The following examples selected from chapter 14 (“Additional

Examples”) have been converted to RPN keystrokes. These examples

illustrate how to convert algebraic to RPN keystrokes in less common

situations: with %, with R, and in a CFLO list.

Example: Simple Interest at an Annual Rate. Your good friend needs a

loan to start her latest enterprise and has requested that you lend her

$450 for 60 days. You lend her the money at 7% simple annual interest,

to be calculated on a 365-day basis. How much interest will she owe

you in 60 days, and what is the total amount owed?

Keys: Display: Description:

450 E 7 % %#&.(" Annual interest.

60 * 365 / .&#*" Actual interest for 60

days.

450 + +..&#*" Adds principal to get

total debt.

Example: APR for a Loan with Fees. A borrower is charged two points

for the issuance of a mortgage. (One point is equal to 1% of the

mortgage amount.) If the mortgage amount is $60,000 for 30 years

and the interest rate is 11½% annually with monthly payments, what

APR is the borrower paying?

1. Since the payment amount is not given, calculate it (PMT) first. Use the

given mortgage amount (PV = $60,000) and interest rate (I%YR =

11½%).

2. To find the APR (the new I%YR), use the PMT calculated in step 1 and

F: RPN: Selected Examples 277

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adjust the mortgage amount to reflect the points paid (PV = $60,000

－2%). All other values remain the same (term is 30 years; no future

value).

Keys: Display: Description:

" ]

#$ 5?@2 H<A"

0EAH"

If necessary, sets 12

payments per year and

End mode.

30 @ T <8%'(&((" Figures and stores number

of payments.

11.5 U

60000 V

5O8'(K(((&(("

Stores interest rate and

amount of loan.

0 X GO8(&((" No balloon payment, so

future value is zero.

W 50:8/.,+&#-" Borrower’s monthly

payment.

R V

2 %- V

5O8.*K*((&(("

Stores actual amount of

money received by

borrower into PV.

U ;6@28##&-'" Calculates APR.

Example: Loan from the Lender’s Point of View. A $1,000,000

10-year, 12% (annual interest) interest-only loan has an origination fee

of 3 points. What is the yield to the lender? Assume that monthly

payments of interest are made. (Before figuring the yield, you must

calculate the monthly PMT = (loan x 12%) ÷ 12 mos.) When calculating

the I%YR, the FV (a balloon payment) is the entire loan amount, or

$1,000,000, while the PV is the loan amount minus the points.

278 F: RPN: Selected Examples

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Keys: Display: Description:

" ]

#$ 5?@2 H<A"

0EAH"

If necessary, sets 12

payments per year and

End mode.

10 @ T <8#$(&((" Stores total number of

payments.

1000000 E

12 %

#$(K(((&(("

Calculates annual interest

on $1,000,000.

12 / W 50:8#(K(((&((" Calculates, then stores,

monthly payment.

1000000 X GO8#K(((K(((&((" Stores entire loan amount

as balloon payment.

3 % - &

5O8/,-(K(((&(("

Calculates, then stores,

amount borrowed (total -

points).

U ;6@28#$&.%" Calculates APR—the yield

to lender.

Example: Savings for College. Your daughter will be going to college

in 12 years and you are starting a fund for her education. She will need

$15,000 at the beginning of each year for four years. The fund earns

9% annually, compounded monthly. You plan to make monthly deposits,

starting at the end of the current month. How much should you deposit

each month to meet her educational expenses?

See figures 14-1 and 14-2 (chapter 14) for the cash-flow diagrams.

Remember to press the = key for E while working in a list.

(Pressing I will add data to the list, not perform an ENTER.)

F: RPN: Selected Examples 279

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Keys: Display: Description:

" r "Displays current cash-flow

list and CFLO menu keys.

p s

G9ECL(T8U"

Clears current list or gets a

new one.

Step 1: Set up a CFLO list.

Keys: Display: Description:

0 I G9ECL#T8U" Sets initial cash flow,

FLOW(0), to zero.

0 I P:;0HFL#T8#" Stores zero in FLOW(1)

and prompts for the

number of times it occurs.

12 E 12 * 1 -

G9ECL$T8U"

For E, press =, not

I. Stores 143 (for

11 years, 11 months) in

#TIMES(1) for FLOW(1).

15000 I P:;0HFL$T8#" Stores amount of first

withdrawal, at end of

12th year.

I G9ECL%T8U"

0 I P:;0HFL%T8#" Stores cash flows of

zero ...

11 I G9ECL+T8U" ... for the next 11 months.

15000 II G9ECL.T8U" Stores second withdrawal,

for sophomore year.

280 F: RPN: Selected Examples

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0 I 11 I G9ECL'T8U" Stores cash flows of zero

for the next 11 months.

15000 II G9ECL-T8U" Stores third withdrawal,

for junior year.

0 I 11 I G9ECL*T8U" Stores cash flows of zero

for the next 11 months.

15000 II G9ECL,T8U" Stores fourth withdrawal,

for senior year.

e E <5OK <4FK <GO"

<HHA ;6"

Done entering cash flows;

gets CALC menu.

Step 2: Calculate NUS for the monthly deposit. Then calculate net

present value.

Keys: Display: Description:

9 E 12 /

;68(&-."

Figures the periodic

(monthly) interest rate and

stores it in I%.

w <4F8#*$&%(" Amount of monthly deposit

needed to meet planned

withdrawals.

v <5O8#-K,-%&+*" Calculates the net present

value of the monthly

deposits, which is the

same as the NPV of the

four future withdrawals.

Example: Tax-Free Account. Consider opening an IRA account with a

dividend rate of 8.175%. 1) If you invest $2,000 at the beginning of

each year for 35 years, how much will you have at retirement? 2) How

much will you have paid into the IRA? 3) How much interest will you

have earned? 4) If your post-retirement tax rate is 15%, what is the

F: RPN: Selected Examples 281

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after-tax future value of the account? Assume only the interest will be

taxed (the principal was taxed before deposit). 5) What is the

purchasing power of that amount, in today’s dollars, assuming an 8%

annual inflation rate?

Keys: Display: Description:

" ]

. 1 Y

Z e

# 5?@2 JH=;<"

0EAH"

Sets 1 payment per year

and Begin mode.

35 T <8%.&((" Stores number of payment

periods until retirement (1

x 35).

8.175 U ;6@28*&#*" Stores dividend rate.

0 V 5O8(&((" Present value of account

(before first payment).

2000 & W 50:8/$K(((&((" Annual payment (deposit).

X GO8%*-K'+(&+." Calculates amount in

account at retirement.

R W R

T *

/-(K(((&(("

Calculates total amount

paid into IRA by

retirement.

R X + %#-K'+(&+." Calculates interest you will

earn.

15 % +-K'+'&(-" Taxes at 15% of interest.

&R X

%%,K,,+&%,

Subtracts taxes from total

FV to calculate after-tax

FV.

X GO8%%,K,,+&%,

Stores after-tax future

value in FV.

282 F: RPN: Selected Examples

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5O8/$$K,,.&%'"

Calculates present-value

purchasing power of the

above after-tax FV at 8%

inflation rate.

Example: Taxable Retirement Account. If you invest $3,000 each year

for 35 years, with dividends taxed as ordinary income, how much will

you have in the account at retirement? Assume an annual dividend rate

of 8.175% and a tax rate of 28%, and that payments begin today.

What will be the purchasing power of that amount in today’s dollars,

assuming 8% annual inflation?

Keys: Display: Description:

" ] "Displays TVM menu.

. 1 Y

Z e

# 5?@2 JH=;<"

0EAH"

Sets 1 payment per year

and Begin mode.

35 T <8%.&((" Stores years until

retirement.

8.175 E 28 %

.&*,"

Calculates interest rate

diminished by tax rate.

U ;6@28.&*," Stores interest rate.

0 V 5O8(&((" Stores no present value.

3000 & W 50:8/%K(((&((" Stores annual payment.

X GO8%+.K.(.&'#" Calculates future value.

0 W

5O8/$%K%'*&##"

Calculates present-value

purchasing power of the

above FV at 8% inflation.

Error Messages 283

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Error Messages

The calculator beeps and displays an error message under certain

circumstances－for example, when you attempt an operation that is not

allowed.

The calculator distinguishes between math errors that occur on the

calculator line and other types of messages by preceding math-error

messages with the word H22E2I.

Press C or < to erase the message and restore the previous

display.

J1A =4HFFHFI

52HFF V792W :E O;HC

The Solver cannot begin a numerical search using the initial estimates.

See pages 180 and 239.

J1:: :EE 9EC :E 52;<:

To conserve battery power, the calculator will not transmit data to the

printer until fresh batteries have been installed.

7422H<: 9;F: 4<<10HAQ

<10H E2 79H12 :MH 9;F:

Attempted to get another list without first clearing or naming the current

list. Press @c to clear it or o to name it.

H05:@ 9;F:

Attempted a calculation using an empty CFLO or SUM list.

H22E2I 9E=12;:M0L<H=T"

H22E2I 9E=12;:M0L(T"

284 Error Messages

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

Attempted to take the base 10 or natural log of a negative number or

zero. This can happen during curve-fitting calculations if you attempt to

calculate:

! A logarithmic forecasting model with a negative or zero x-value.

! An exponential model with a negative or zero y-value.

! A power model with a negative or zero x- or y-value.

H22E2I <H=\<E<;<:H=H2"

Attempted to raise a negative number to a non-integer power.

H22E2I EOH2G9EC"

An internal result in a calculation was too large for the calculator to

handle.

H22E2I FY2:L<H=T"

Attempted to take the square root of a negative number or calculate

G.SD given any negative frequencies.

H22E2I 4<AH2G9EC"

An internal result in a calculation was too small for the calculator to

handle.

H22E2I (\<H="

Attempted to raise zero to a negative power.

H22E2I (D("

Attempted to divide zero by zero.

H22E2I (\("

Attempted to raise zero to the zero power.

H22E2I D("

Attempted to divide by zero.

;<54:F 714FHA D("

Error Messages 285

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

The numbers stored into built-in variables caused a division by zero in

the calculation. You must change one or more stored values. (Refer to

the equations in appendix B to see which variables appear in the

divisor.)

;<F4GG;7;H<: A1:1"

! Attempted to calculate standard deviation with only one value in the

list.

! Attempted to do curve fitting using an x-variable list in which all the

values are equal.

! Attempted to do curve fitting using the logarithmic or power models

with a list for which the transformed values of x (ln x) are equal.

;<F4GG;7;H<: 0H0E2@"

The calculator has insufficient memory available to do the operation

you’ve specified. Refer to “Managing Calculator Memory” on page

227 for additional information.

;<:H2HF: Z8 /#((6"

One of the following values for interest is less than or equal to－100:

! TVM menu: I%YR ÷ P/YR.

! PER menu: NOM% ÷ P (calculating EFF%); EFF% (calculating

NOM%).

! CONT menu: EFF%.

! CFLO menu: I% (calculating NPV, NUS, or NFV) or estimate of IRR%.

;<:H2245:HA"

Calculation of I%YR, IRR%, amortization results, a Solver variable, or

a SUM-list sort was interrupted.

;<O19;A A1:H"

286 Error Messages

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

! The number entered cannot be interpreted as a proper date. Check its

format (page 143).

! Attempted to set a date outside the range 1/1/2000 through

12/31/2099, or attempted date arithmetic outside the range

10/15/1582 through 12/31/9999.

;<O19;A HY41:;E<"

! The Solver cannot interpret the equation due to a syntax error. Refer to

“What Can Appear in an Equation,” page 166.

! A variable’s name is invalid. Refer to “Names of Variables,” page

166.

;<O19;A ;<54:"

! Attempted to store into a built-in variable a number that is outside the

range of values permitted for that variable.

! The number entered cannot be interpreted as a proper time.

! The appointment’s repeat interval is out of range.

! Attempted to enter a non-integer, negative number when specifying

the number of displayed decimal places (in DSP).

;<O19;A <"

Attempted to calculate I%YR with N ≦ 0.99999 or N ≧ 1010.

;226 [ ( HX;F:FQ 3H@"

;< =4HFFQ VF:EW R;226S"

Calculation of IRR% produced a negative answer, but the calculator has

determined that there is also a unique positive answer. (Refer to page

238.)

017M;<H 2HFH:"

The calculator has been reset (page 224, 228).

Error Messages 287

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

01<@ E2 <E FE94:;E<F"

The calculator is unable to calculate I%YR. Check the values stored in PV,

PMT, and FV. Make sure the signs of the numbers are correct. If the

values of PV, PMT, and FV are correct, the calculation is too complex for

the TVM menu. You may be able to perform the calculation using the

CFLO menu to calculate IRR%.

01<@?<E FE94:;E<FQ 3H@"

;< =4HFFQ VF:EW R;226S"

The calculation of IRR% is complex, and requires you to store a guess.

(Refer to page 238.)

0H0E2@ 9EF:"

Continuous Memory has been erased (page 224, 230).

<10H 292H1A@ 4FHAI"

:@5H 1 <10HQ V;<54:W"

The list name you’ve attempted to enter is already in use; type in a new

name and press I.

<E FE94:;E<"

No solution is possible using the values stored in the current built-in

menu or list. This most commonly results from an incorrect sign for a

cash flow or other monetary value. (Review page 64.)

<a <Z( E2 < <E<;<:H=H2"

Attempted to calculate the factorial of a negative or non-integer value.

EOH2G9EC"

A warning－not an error－that the magnitude of a result is too large for

the calculator to handle, so it returns ±9.99999999999E499 rounded

to the current display format. See page 47 for limits.

FE94:;E< <E: GE4<A"

288 Error Messages

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

No solution was found for a Solver equation using the current values

stored in its variables. Refer to page 246 in appendix B.

4<AH2G9EC"

A warning－not an error－that the magnitude of a result is too small for

the calculator to handle, so it returns the value zero. See page 47 for

limits.

4<HY419 9;F: 9H<=:MF"

Attempted a two-list SUM calculation using lists of unequal lengths.

Index 289

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Index

#Special Characters

-, 47

low-battery annunciator,

17, 184, 224

shift annunciator, 19

%, 40

%TOTL menu

formula, 247

using, 51

&, 22

Σ, 139, 171, 176–77, 220

G, 35

F, 35

^, 78

q, 92, 95, 96–97

s, 127

J, 49, 50

K, 49, 51

Q, 51

¢, 132, 139

£, 132, 139

¤, 132, 139

¥, 132, 139

¦, 132, 139

_, 144

`, 144

], 143

2, 42

-, 150

®, 150

() alarm annunciator, 147

J menu

formula, 247

using, 50

´ or ³, 174

B, C, A,

@, 32

@, 19

] or [, 43, 269

editing a list, 98

in a list, 96, 162

with history stack, 43

<, 20, 32, 272

=, 174

t, 41

v, 16, 17, 262

print annunciator, 184

#TIMES, 96–97

1N" , D, 56

‰, 115

Š, 115

290 Index

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

0, 36, 262

€, 109

, key, 34

c through d, 145

[, appointment-setting

menu, 145

ABS (absolute value) function,

169

Accrued interest, on bond, 109,

111

Accuracy of the clock, 231

Acknowledging appointments,

147

Actual calendar

actuarial equations, 246

for arithmetic, 149

for bonds, 110

Addition, 21

ADJST menu, 144

Advance payments, 74–77,

199–200, 253. See also

Leasing

Algebraic

mode, 36, 262

rules in equations, 164–66

ALOG, 169

Alphabetic keys, 30–32

ALPHAbetic menu, 30

AM/PM format, 143

Amortization

calculations, 77–81

equations, 247

schedule, 78

schedule, printing, 81–83

AMRT menu, 78

AND operator, 166, 174

Annual percentage interest rate

in TVM, 63

with fees, 193

with fees, RPN, 276

Annunciators, 18

definition, 18

printer, 184

Antilogarithms, 42, 169

Appointment

menus, 142, 145

messages, 146

repeat interval, 147, 148

-setting menu, 146

Appointments

acknowledging, 147

clearing, 148

messages, 145

past due, 146

printing, 188

setting, 146–47

unacknowledged, 146, 148

APPT menu, 145

APR for, with fees, RPN, 276

calculations, 67–71

interest-only, 194

interest-only, RPN, 276

odd-period, 195, 196–97

Arithmetic, 21–22, 38

in registers and variables, 46

in RPN, 264–67, 270

in RPN stack, 270

Index 291

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RPN examples, 275

Arithmetic priority, 154

Arrow keys

for changing current equation,

156

for editing, 32

for finding an equation, 162

for rolling the history stack,

for viewing long equations,

166

E, 56

›, 132

a, 78

Z, 64

†, 115

R, 56

Backspace key, 20

Balance of loan, 80–81

Balloon payment, 69–71

Batteries, changing, 225–26

Battery life, 224

annunciator, 224

Beeper, 147

Beeper on and off, 36

Begin payment mode, 64, 66

Beginning of list

in CFLO list, 98

in SUM list, 124

Bond calculations, 110–13

equations, 249

fractional values for, 111

price, 111

type, 109, 110

yield, 111

BOND menu, 108–9

Bonds, 215–16

Bottom

of the current list, in CFLO,

of the Solver list, 162

Braces in equations, 167

Brackets in equations, 167

Brightness of the display, 17

Built-in variables. See Variables,

built-in

BUS menu, 49, 254

Business variables, clearing, 50

Buy option, for a lease, 75–77

B-value, in curve fitting, 132

%CHG menu, 50

in CFLO menu, 92

in SOLVE menu, 157

in SUM menu, 122

in TIME menu, 142

}, 109

~, 109

™, 132

8, 55

292 Index

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

9, 55

U, 56

V, 56

) key, 53

=, F, 56

@c, 20, 28–29

C, 17, 20, 32

v, 16, 17, 262

CALC menu

in CFLO menu, 101

in SOLVE menu, 158–59

in SUM menu, 128

in TIME menu, 150

Calculations, RPN

order of, 274

parenthesis in, 266, 274

Calculator

not functioning, 231–32

resetting, 225, 228–30

Support, 222

Calculator line

arithmetic in, 38–48

definition, 18

displaying alphabetic

information, 31–32

editing, 20

Calendar. See also Date

360-day, 150

365-day, 150

actual, 150

range of, 149

Calendar basis, 108–9

Call, 110 , 112

Canadian mortgage, 197–99,

252

Capitalized value, lease,

74–75

Cash flow

calculations, 91–107

equations, 248

list. See CFLO list

Cash flow diagrams

in cash flow calculations,

92–94

in TVM calculations, 64–66

Cash flows

equal. See Cash flows,

grouped

grouped, 94, 104

initial, 94, 95

maximum number of, 91

sum of, 101

ungrouped, 93

zero, 94, 95

CDATE, 169

CFLO list

CALC menu, 101

clearing, 99

copying from, 98

correcting, 97

creating, 94

definition, 91

deleting numbers, 98

editing, 92, 97

entering numbers in, 95–97

GETting a new list, 99

inserting numbers, 98

name, clearing, 99

naming, 98–99

printing, 187

Index 293

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signs of numbers, 92

starting a new list, 99

viewing name of current list,

viewing numbers, 97

Chain calculations, 21, 38–39,

in RPN, 266, 274

Changing

batteries, 225–26

the sign of a number, 22

Characters

for CFLO list, 98–99

for equation names, 161

for SUM list, 126

in equations, 166–67

inserting and deleting,

31–32

Chi-squared, 219–20

Clearing, 20

%CHG variables, 50

%T variables, 50

AMRT variables, 80

appointments, 146, 148

BOND variables, 109

BUS variables, 50

calculator memory, 28–29

CFLO lists, 95, 99

ICNV variables, 86

menu variables, 28

menus, 28

MU%C variables, 50

MU%P variables, 50

numbers in RPN, 272

Solver variables, 163

SUM lists, 123

the history stack, 44

the RPN stack, 269, 272

TIME CALC variables, 150

TVM variables, 64

variables, 28–29

Clock. See Time

Commas, in numbers, 35

Compound interest calculations,

Compounding

annual, 71

monthly, 67, 68, 74, 75

periods, 61, 62, 63, 64

periods, vs. payment periods,

87–90, 200

rates, 84

semimonthly, 72

Conditional expressions,

174–76

Constant numbers, RPN, 271,

272

Constants in equations, 166

CONT menu, 86

Continuous compounding,

calculating interest for, 85

Continuous Memory, 37

erasing, 225, 230

using, 17

Contrast of display, changing,

Conventional investments,

definition, 101

Converting interest rates,

85–87

294 Index

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Correlation coefficient, 132

Cost

markup on, 49, 52

of capital, 101

Counter variable,in summation

function, 176

Coupon

basis, 108–9

payments, 108

Creating

a CFLO list, 94–96, 99

a new equation, in the Solver,

157–58

a SUM list, 123–24, 127

CTIME, 169

Cube root, 41

in RPN, 265

Currency

clearing variables, 60

converting, 59

entering a rate, 57

exchange, 57, 58

selecting, 55

storing and recalling, 59

Currency#1, 55

Currency#2, 55

Current equation, 156

deleting, 162–64

printing, 187

CURRX menu, 55, 255

Cursor, 19

movement keys, 32

Curve fitting, 121, 132–34

calculations, 134–37

equations, 251

Customer Support, 222

in CFLO menu, 92

in Solver menu, 157, 164

in SUM menu, 122, 127

•, 115

?, 32

ª, 150

«, 150

¬, 150

in appointment-setting menu,

145

in SET menu, 143

A, 56

/, 185

", 18

D, 34–35

Date

in the past or future, 151

setting, 143–44

viewing, 141, 169

Date arithmetic, 149–52

Date format, 143, 144

for appointments, 144

DATE, Solver, 169

Day of the week, determining,

149

Day.month.year format, 143,

Index 295

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144

DDAYS, 169

Decimal places, 34, 47

Decimal point, 35

Declining balance depreciation.

See Depreciation

Deleting

all information, 225,

228–31

characters, 32

equations, 162–64

from a CFLO list, 98, 100

from a SUM list, 125, 127

variables in the Solver,

162–64

Dependent variable, 134

DEPRC menu, 114

Depreciation

ACRS method, 114, 118–19

calculations, 114–17

declining balance method,

114, 116 –17

equations, 250

partial year, 118 –19

straight line, 114, 116

sum of the years’ digits, 114,

116

Diagnostic self-test, 232–33

Diagrams, cash flow, 64–66,

92–94

Digit separator, 35

Direct solutions in Solver, 179,

240–41

Discount rate, 101

Display

clearing, 20

contrast, 17

format, 34

in RPN, 268–73

messages, 36

organization, 19, 43

printing the contents of, 185

turning on and off, 17

Displayed messages, 283

Displaying

the contents of registers,

43–46

values assigned to variables,

Division, 38–40

Doublespace printing, 36, 185

DSP menu, 34–35, 260

\ key, 47

[, 64

I, 42

*, 157, 161

<, 56

$, 18

%, 18

k key, 88

e, 25, 28, 92, 96, 123, 147,

161

E, 263, 264–65, 271,

274

E, in numbers, 47

296 Index

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Editing

alphabetic information,

31–32

equations, 161

keys, 31–32

Effective interest rate, 84–87,

100

End payment mode, 64, 65

Ending value, in summation

function, 176

English language, setting, 224

Entering

equations, 157–58

guesses in the Solver,

181–83

Entering numbers

in a SUM list, 123–24

in RPN, 264, 271

into CFLO lists, 95–97

Environmental limits, 231

Equals sign, used to complete

calculations, 21, 38

Equation list. See Solver list

Equation Solver, 153–83,

240–46

clearing, 163

introduction, 29

Equations

algebraic rules, 164

characters in, 166–67

clearing, 163

deleting, 162–64

displaying, 162

editing, 161

entering, 157

erasing, 163

for built-in menus, 246–53

invalid, 158

length of, 153

long, viewing, 166

naming, 161

verifying, 157–58

writing, 164

Erasing. See also Clearing;

Deleting

Erasing calculator memory, 225,

230–31

Error messages, 36, 283

Estimates, entering in the Solver,

181–83

Examples, 190

in RPN, 276–82

Exchanging registers, RPN, 269

EXP, 169

EXPM, 169

Exponential model, 130, 132,

133

Exponential numbers, 47

Exponentiation, 41–42, 265

in equations, 165

Œ, 115

—, 128

&, 18

Index 297

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X key, 63

+ key, 34

Face value, bond, 110

FACT, 169

Factorial, 42, 169

FIN menu, 256–57

FLOW, Solver, 169

Forecasting

calculations, 130–37

equations, 251

values, 121, 132–34

Foreign language, 224

Formatting number, 34

FP, 169

Fractional part, 169

FRCST menu, 130, 132

Functions in equations, 167,

168–71

Future date, calculating, 151

Future value of a series of

payments

equation, 246

Solver function, 171

g, 82

, 132

p, in CFLO, 99

p, in SUM, 127

General business

calculations, 49–53

equations, 247

Grouped standard deviation,

138–39

Guesses

entering in the Solver,

181–83

IRR%, entering, 238–40

Solver, 245

in the appointment-setting

menu, 145

in the SET menu, 143

I, 56

Halting a numerical search,

180

Hierarchy of menus, 24

Hierarchy of operations, in

equations, 165

History stack, 43. See also

Stack, RPN

printing, 186

HMS, 170

HP Solve. See Solver

HRS, 170

Humidity requirements, 231

_, 78

in CFLO list, 92, 98

in SUM list, 122, 124

298 Index

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

t, 101

u, 101

', 18

U key, 63

S, G, 56

I, 98

for storing equations, 30

in CFLO menu, 92

in RPN, 264

in the Solver list, 157–58

in SUM list, 123

I%, 101

ICNV

equations, 248

menu, 84–85

variables, clearing, 86

IDIV, 170

IF, 170, 174–76

nested, 175

Independent variable, 134

Individual Retirement Account,

72–73

Inserting characters, 32

Installing batteries, 225–26

Insufficient memory, 37, 227

Insurance policy, price,

213–15

INT, 170

INT, rounded in amortization

calculations, 78

Interest

compound, 61, 84

equation, 248

on loan, amount of PMT

applied toward, 80–81

simple, 61

Interest rate conversions,

84–90, 201, 248

effective and nominal, 84

Intermediate results, RPN, 268,

274

Internal rate of return. See also

IRR%

calculations, 91, 97,

100–101

Interrupting an IRR% calculation,

239

Interrupting the Solver, 180

INV, 170

Invalid equation, 158

Inverse, 265

Investments

calculating IRR% and NPV of,

101–4

with grouped cash flows,

104–5

IP, 170

IRA, 72–73, 206

IRR%, 100, 101, 209

IRR% calculations, 238–40

halting, 239

IRR% estimate

making, 239–40

seeing current, 239

IRR% solutions, types of,

238–39

Index 299

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ITEM, 170

Iteration in Solver, 179–83,

240, 242–46

ˆ, 115

•, 132

k, 186

o, 42

3, 42

L, 44

in RPN, 273

Language, setting, 224

Large number

available, 47

in a list, 128

Large numbers, keying in and

displaying, 47

Last result, copying, 44

LAST X register, RPN, 273

Leasing, 74–77, 199–200

LEFT-RIGHT, interpreting,

242–46

Letter keys, 30

Linear estimation, 121,

132–34

Linear model, 130, 133

Linear regression, 121

List. See CFLO list; SUM list;

Solver list

List, RPN, 264

rolling the stack, 269

LN, 170

LNP1, 170

Loan

amortizing, 77–83

APR for, with fees, 193

LOG, 170

Logarithmic model, 130, 132,

133

Logarithms, 42, 170

Logical operators, 174

Low memory, 227

Low power, 224

and printing, 184

annunciator, 184

š, 132

|, 109

+, 49, 53

6, 52, 128

‘, 128

”, 128

•, 128

œ, 132

in appointment setting menu,

145

in printer men, 186

\, 143

N, 56

300 Index

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

) key, 25

@A, 22–26

@M, 37

MAIN menu, 19

Manual, organization of, 16

Markup

on cost, 49, 52

on price, 49, 52

Math in equations, 165, 167

MATH menu, 42, 260

MAX, 170

Mean, 251

calculating, 128–30

weighted, 138–39

Median, 251

calculating, 128–30

Memory. See also Continuous

Memory

freeing, 227

insufficient, 227

losing, 225, 230

using and reusing, 37

labels, 19

maps, 25, 254–60

Menus

calculations with, 27–28

changing, 25, 28

exiting, 28

names of, 161

printing values stored in,

186–88

sharing variables, 53

Messages for appointments,

146

Messages, error, 283

MIN, Solver, 170

MOD, 170

Mode of payments (Begin and

End), 64

Models, curve-fitting, 132, 133

Modes

1, 36, 261–62, 265

0, 36, 261, 262

@>, 185

beeper, 36

double-space printing, 36,

185

menu map, 260

printer ac adapter, 36

Modified IRR, 209–12, 253

Month/day/year format,

143–44

Mortgage, 68, 69. See also

Loan

calculations, 67–71, 77–80

discounted or premium, 191

Moving average, 217–19

MU%C, 50

equation, 247

MU%P, 50

equation, 247

Multiple equations, linking, 178

Multiplication

Index 301

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in arithmetic, 21, 38–40

in equations, 165

O, 56

b, 78

S, 63

in CFLO list, 98–99

in SUM list, 126

v, 101

w, 101

x, 101

/, 157

@, 56

B, 56

J, 56

4, 42

j, 85–86

@ S, 63

N, non-integer, 63, 72

Names

of equations, 161

of lists, clearing, 99

of variables, 166

Negative numbers

in arithmetic calculations, 22

in cash-flow calculations,

92–94

in TVM calculations, 64

Neighbors in Solver, 243

Nested IF function, in the Solver,

175

Net future value, 91, 101

Net present value, 91, 101

Net uniform series, 91, 101

NFV

calculating, 91, 101

equation, 249

Noise Declaration, 237

Nominal interest rate, 84–87,

100

Non-integer period, 172

NOT, 174

Notes, discounted, 216–17

NPV

calculating, 100–101

equation, 100, 248

Number

lists. See CFLO list; SUM list;

Solver list

of days between dates,

149–51

of decimal points, 47

of payments, in TVM, 62

range, 48

Numbers. See also Value

entering, RPN, 264, 271

with exponents, 47

Numerical solutions, 179–81

NUS, 100, 249

M, 50

@o, 17

302 Index

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O, 17

Odd-period calculations,

172–73, 195, 253

Operators, in equations,

164–67

in RPN, 266, 268, 274

Option to buy, for a lease,

74–75

OR, 174

Order of calculation, in the

Solver, 165

OTHER menu, 146–47

Overdue appointments. See

Past- due appointment

Overview, 3

H, 56, 63

`, 78

W, 63

Y, 62

^, 78, 82, 85

*, 52, 109

P, 51

ž, 121, 132

T, 56

5, 42

(, 18

@p, 186

P, 186

Parentheses

in arithmetic calculations,

39–40

in equations, 165, 167

in RPN, 266, 268, 274

Partial period. See also Odd

period

payments, 62

Past dates, calculating, 151

Past due appointments

acknowledging, 148

definition, 146

Payment mode, 62

changing, 62

definition, 65–66

resetting, 62

Payment periods, 62

compounding, 61–64

in cash flow calculations, 93

vs. compounding periods,

87–90, 200

Payments

amortization, 77–81

lease, 74–77

number per year, in TVM, 63

TVM, 62

Percent, 40

change, 49–51

key for simple interest, 40,

of cost, 49, 52

of total, 49, 51

Percentage calculations, 49–53

in RPN, 265

Periodic compounding,

calculating interest rates for,

Index 303

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85–86

Periodic interest rate, 101

Periodic rate of return, 100

Periods, 35. See also Payment

periods in numbers

in numbers, 35

PI, 42, 170

PMT. See also Payments

in TVM, 63

rounded amortization

calculations, 78

Positive numbers

in cash flow calculations,

92–94

in TVM, 64

Power. See also Low power;

Batteries

function, 41, 265

raising a number to, 41

Power curve, 130, 132, 133

Power on and of, 17

Precision of numbers, internal,

Present value

definition, 63

of a lease, 74–77

of a series of payments, 171,

246

of a single payment, 171,

246

Previous menu, displaying, 28

PRICE, as a shared variable, 53

Price, markup on, 49, 52

Principal of loan, amount of

PMT applied toward,

80–81

Printer

power for, 185

using, 184

PRINTER menu, 186, 260

Printer port, 184

Printing

amortization table, 81–83

appointments, 188

display, 185

double space, 36, 185

equations, 187

history stack, 186

interrupting, 189

messages, 188

number lists, 187

slow, 184

Solver list, 187

speed, 185

statistical values, 186

time and date, 186

variables, 187

with tracings, 188

Prompting for #TIMES, 96

Purchase date, bond, 109

Purchase price, in mortgage

calculation, 68–69

PV, rounded in amortization

calculations, 78

Questions, common, 222–24

304 Index

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“, 128

b, 145

7, 55

K, 56

P, 56

1, 36

m, 186

R, 56

@r, 35

~, 43, 263

R, 45–46, 98

in RPN calculations, 266

with variables, 28

R↑, 263

Radix (decimal point), 34

Range

calculating, 128

of numbers, 48

Rate of return, periodic, 100

Recalling numbers, 45–46

from variables, 28

in RPN, 264, 266

with @L, 44

Reciprocal key, 41

Registers

arithmetic in, 46

in RPN, 268–73

printing the contents of, 186

Relational operators, 174

Remaining depreciable value,

115 , 116

Renaming lists. See CFLO list;

SUM list; the Solver list

Repeating appointments

past-due, 148

setting, 147

Replacing batteries, 225–26

Required rate of return, 101

Resetting the calculator, 228

Reusing

a number, RPN, 271, 273

calculator memory, 37, 230

Reverse Polish Notation, 261

RND, 170

Rounding a PMT, 71

Rounding numbers, 35

RPN. See appendixes D, E, and

F, or individual entries

Running total, 123–24

•, 115

{, 109

‡, 115

Ž, 115

’, 128

–, 128

©, 142

:, 55

?, 56

Index 305

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

C, 56

Q, 56

l, 186

¡, 132

@S, 34

s, 45–46

calculations with, RPN, 266

S (function), 170

Sample standard deviation,

128

Saving numbers, 43

Savings account, 71–72

college, 202–6

college, RPN, 278

regular, 200–202

retirement, 208

retirement, RPN, 282

tax free, 206–9

tax free, RPN, 280

Savings calculations, 71–73

Scientific notation, 47

Self-test, 232–33

Service, 235–36

SET menu, 143

Setting a language, 18, 37

Setting an appointments,

146–47

Settings, default start-up, 230

Settlement date, 109

SGN, 170

Shared variables

in BUS, 53

in equations, 162

in ICNV, 86

Shift, 19

Sign of numbers

in cash-flow calculations, 92

in TVM calculations, 64

Simple interest, 40

with annual rate, 190

with annual rate, RPN, 276

Slope, in curve-fitting, 132,

134

Small numbers, keying in and

displaying, 47

Smallest number

available, 47

in a list, 128

SOLVE menu, 260

Solver, 153–83. See also

Equations

Solver calculations, 155,

158–59

creating custom menus,

153–54

how it works, 179–83

multiple solutions in, 179

technical discussion of,

240–46

using, 153–68

Solver estimates, seeing curren,

240–46

Solver functions, 168–71

Solver list

clearing, 162–64

current equation, 156

306 Index

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definition, 153

deleting equations, 157,

162–64

deleting variables from,

162–64

editing an equation, 157

empty, 156

entering equations, 157–58

printing, 187

Solver menu, 156–57

for multiple equations, 178

Solver solutions, types of,

243–46

Solver variables. See Variables,

Solver

Sorting numbers, 128

Spaces in equations, 166

Specifying the number of

decimal places, 34

SPFV, 171, 246

SPPV, 171, 246

SQ, 171

SQRT, 171

Square root

calculating, 41, 265

Solver, 171

Square, Solver, 171

Squaring a number, 41, 265

Stack. See History stack

Stack, RPN, 268–73

automatic movement of, 270,

274

clearing, 269, 273

dropping, 270

lifting, 270

losing contents off the top,

270

replicating contents in, 269,

270

rolling contents, 270, 271

size, 269

Standard deviation, 128–30

calculating, 128–30

grouped, 138–39

Starting value, in summation

function, 176

Statistical calculations, 127–40

Statistical equations, 250–52

Statistical variables, 128,

130–34

Statistics, x and y, 130–34

Step size, in summation function,

176

Storage registers, 45–46

arithmetic in, RPN, 46

printing the contents of, 186

Storing numbers, 44, 45–46

in built-in variables, 28

in RPN, 264, 266

Subtraction, 21, 38–40

SUM equations, 251

SUM items, maximum number

of, 121

SUM list

CALC menu, 128

clearing, 127

clearing numbers, 124

copying a number from, 126

Index 307

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

correcting, 124

creating, 123–24

definition, 121–22

deleting numbers, 125

editing, 122, 124–25

entering numbers in, 123–24

FRCST menu, 132

GETting a new list, 127

inserting numbers, 124

largest number in, 128

name, deleting, 127

naming, 126

printing, 187

smallest number in, 128

sorting, 121, 128

starting a new list, 127

viewing numbers, 124

viewing the name of the

current list, 126

SUM menu, 122–23, 258

Sum of cash flows, 101

Summation, 132, 139, 171,

176–77

function, in the Solver,

176–78, 220

of lists, 177

values, 132, 139

Switching menus, 25–26

#T, 171

#TIMES, prompting, 96–97

%TOTL, 49, 51

in appointment-setting menu,

145

in PRINTER menu, 186

in SET menu, 143

c, 78

O, 51

of a SUM list, 122, 128

z, 109

¯, 150

n, 186

O, sum of cash flows, 101

Text, printing (MSG), 186

Time

accuracy, 231

and date, printing, 186

changing, 143–44

format, 144, 145–46

of day, viewing, 141

setting, 143–44

TIME menus, 141–42

Time value of money

calculations, 61–83

equations, 247

Top of the equation list, in the

Solver, 162

Total, percent of, 51

Trace-printing, 188

TRN, 171

Troubleshooting, 222–24

True population standard

deviation, 128

Truncating function, in Solver,

171

308 Index

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

Turning calculator on and off,

TVM

calculations, 61–83

equation, 247

instructions, 66–67

menu, 61–64, 66

variables, clearing, 64

Typing aids, 167

Typing alphabetic characters,

;, 56

>, 56

Unacknowledged appointments,

148

Unit conversions, in the Solver,

178

Unknown variables in Solver,

240, 241

Up-arrow key, 43

USFV, 171, 246

USPV, 171, 246

Values

clearing, 28–29. See also

recalling, 28, 45–46

storing, 28, 45–46

transferring between menus,

Variable,

dependent, 134

independent, 134

Variables

statistical, 130–34

Variables,

built-in, 27

printing, 187

statistical, 128

Variables, Solver, 154

clearing, 163

deleting, 163

names of, 166

shared, 162

Variables,shared, 53

Verifying equations, 157–58

Viewing lists. See CFLO list;

SUM list; Solver list

Ÿ, 132

L, 56

Warranty, 233–35

Weighted mean, 132, 138–39

v, 41

x, 43

in RPN, 269

XOR, 174

x-values, in forecasting,

133–34

Index 309

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

•, 109

‹, 115

M, 56

u, 41, 265

Yield

of lease, 74–75

to call, bonds, 108

to maturity, bond, 108

y-intercept, in curve-fitting, 132,

134

y-values, in forecasting,

133–34

Zero-coupon bond, 113

File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11

This regulation applies only to The Netherlands

Batteries are delivered with this

product, when empty do not throw

them away but collect as small

chemical waste.

Bij dit produkt zijn batterijen

geleverd. Wanneer deze leeg zijn,

moet u ze niet weggooien maar

inleveren als KCA.

Hp 17Bii Users Manual Plus E PRINT 030709

HP 17bII+ to the manual 45ec1dea-d755-48e0-88ed-e972f9ecd5c9

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