# HP 12c_user's Guide_English_HDPMBF12E44 Guide_English_E_HDPMBF12E44 C00363319

### If not then c00363319 Manual: ://h10032.www1.hp.com/ctg/Manual/c00363319

### HP 12C Financial Calculator 0012C-90001 c00363319

User Manual: HP hp 12c_user's guide_English_E_HDPMBF12E44

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hp 12c financial calculator

user's guide

H

Edition 4

HP Part Number 0012C-90001

2

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Notice

REGISTER YOUR PRODUCT AT: www.register.hp.com

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,

NON-INFRINGEMENT 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.

© Copyright 1981, 2004 Hewlett-Packard Development Company, L.P.

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

written permission of Hewlett-Packard Company, except as allowed under the

copyright laws.

Hewlett-Packard Company

4995 Murphy Canyon Rd,

Suite 301

San Diego, CA 92123

Printing History

Edition 4 August 2004

3

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Introduction

About This Handbook

This hp 12c user's guide is intended to help you get the most out of your

investment in your hp 12c Programmable Financial Calculator. Although the

excitement of acquiring this powerful financial tool may prompt you to set this

handbook aside and immediately begin “pressing buttons,” in the long run you’ll

profit by reading through this handbook and working through the examples it

contains.

Following this introduction is a brief section called Making Financial Calculations

Easy—which shows you that your hp 12c does just that! The remainder of this

handbook is organized basically into three parts:

z Part I (sections 1 through 7) describes how to use the various financial,

mathematics, statistics, and other functions (except for programming)

provided in the calculator:

z Section 1 is about Getting Started. It tells you how to use the keyboard,

how to do simple arithmetic calculations and chain calculations, and

how to use the storage registers (“memories”).

z Section 2 tells you how to use the percentage and calendar functions.

z Section 3 tells you how to use the simple interest, compound interest, and

amortization functions.

z Section 4 tells you how to do discounted cash flow analysis, bond, and

depreciation calculations.

z Section 5 tells you about miscellaneous operating features such as

Continuous Memory, the display, and special function keys.

z Sections 6 and 7 tell you how to use the statistics, mathematics, and

number-alteration functions.

z Part II (sections 8 through 11) describe how to use the powerful

programming capabilities of the hp 12c.

z Part III (sections 12 through 16) give you step-by-step solutions to specialized

problems in real estate, lending, savings, investment analysis, and bonds.

Some of these solutions can be done manually, while others involve running

a program. Since the programmed solutions are both self-contained and

step-by-step, you can easily employ them even if you don’t care to learn how

to create your own programs. But if you do start to create your own

programs, look over the programs used in the solutions: they contain

examples of good programming techniques and practices.

4 Introduction

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z The various appendices describe additional details of calculator operation as

well as warranty and service information.

z The Function Key Index and Programming Key Index at the back of the

handbook can be used as a handy page reference to the comprehensive

information inside the manual

Financial Calculations in the United Kingdom

The calculations for most financial problems in the United Kingdom are identical to

the calculations for those problems in the United States — which are described in

this handbook. Certain problems, however, require different calculation methods in

the United Kingdom than in the United States. Refer to Appendix F for more

information.

For More Solutions to Financial Problems

In addition to the specialized solutions found in Sections 12 through 16 of this

handbook, many more are available in the optional hp 12c Solutions Handbook.

Included are solutions to problems in lending, forecasting, pricing, statistics,

savings, investment analysis, personal finance, securities, Canadian mortgages,

learning curves in manufacturing, and queuing theory. A Solutions Handbook is

available online (www.hp.com/calculators).

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Contents

Introduction.................................................................... 3

About This Handbook.....................................................................3

Financial Calculations in the United Kingdom.....................................4

For More Solutions to Financial Problems...........................................4

Part I. Problem Solving ......................................... 15

Section 1: Getting Started............................................. 16

Power On and Off........................................................................16

Low-Power Indication..............................................................16

The Keyboard ..............................................................................16

Keying in Numbers ................................................................17

Digit Separators ....................................................................17

Negative Numbers ................................................................17

Keying in Large Numbers .......................................................18

The CLEAR Keys ....................................................................18

Simple Arithmetic Calculations .......................................................19

Chain Calculations .......................................................................20

Storage Registers..........................................................................23

Storing and Recalling Numbers...............................................23

Clearing Storage Registers......................................................24

Storage Register Arithmetic .....................................................24

Section 2: Percentage and Calendar Functions................ 26

Percentage Functions.....................................................................26

Percentages ..........................................................................26

Net Amount..........................................................................27

Percent Difference..................................................................27

Percent of Total......................................................................28

Calendar Functions.......................................................................29

Date Format..........................................................................29

Future or Past Dates................................................................30

Number of Days Between Dates ..............................................31

Section 3: Basic Financial Functions............................... 32

The Financial Registers ..................................................................32

Storing Numbers Into the Financial Registers .............................32

Displaying Numbers in the Financial Registers...........................32

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Clearing the Financial Registers .............................................. 33

Simple Interest Calculations........................................................... 33

Financial Calculations and the Cash Flow Diagram.......................... 34

The Cash Flow Sign Convention.............................................. 36

The Payment Mode ............................................................... 37

Generalized Cash Flow Diagrams........................................... 37

Compound Interest Calculations..................................................... 39

Specifying the Number of Compounding Periods and the Periodic

Interest Rate ......................................................................... 39

Calculating the Number of Payments or Compounding Periods ... 39

Calculating the Periodic and Annual Interest Rates..................... 43

Calculating the Present Value ................................................. 44

Calculating the Payment Amount............................................. 46

Calculating the Future Value ................................................... 48

Odd-Period Calculations ........................................................ 50

Amortization ............................................................................... 54

Section 4: Additional Financial Functions ....................... 57

Discounted Cash Flow Analysis: NPV and IRR ................................. 57

Calculating Net Present Value (NPV) ....................................... 58

Calculating Internal Rate of Return (IRR) ................................... 63

Reviewing Cash Flow Entries................................................... 64

Changing Cash Flow Entries................................................... 65

Bond Calculations ....................................................................... 66

Bond Price ............................................................................67

Bond Yield ............................................................................67

Depreciation Calculations ............................................................. 68

Section 5: Additional Operating Features ....................... 70

Continuous Memory..................................................................... 70

The Display................................................................................. 71

Status Indicators ................................................................... 71

Number Display Formats ....................................................... 71

Scientific Notation Display Format........................................... 72

Special Displays ................................................................... 73

The key ..............................................................................74

The Key..............................................................................74

Arithmetic Calculations With Constants.................................... 75

Recovering From Errors in Digit Entry ....................................... 75

Contents 7

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Section 6: Statistics Functions........................................ 76

Accumulating Statistics..................................................................76

Correcting Accumulated Statistics ...................................................77

Mean .........................................................................................77

Standard Deviation.......................................................................79

Linear Estimation ..........................................................................80

Weighted Mean...........................................................................81

Section 7: Mathematics and Number-Alteration Functions 83

One-Number Functions .................................................................83

The Power Function.......................................................................85

Part II. Programming ............................................. 87

Section 8: Programming Basics ..................................... 88

Why Use Programs?.....................................................................88

Creating a Program......................................................................88

Running a Program.......................................................................89

Program Memory .........................................................................90

Identifying Instructions in Program Lines ....................................91

Displaying Program Lines........................................................92

The 00 Instruction and Program Line 00 ............................93

Expanding Program Memory ..................................................94

Setting the Calculator to a Particular Program Line .....................95

Executing a Program One Line at a Time.........................................96

Interrupting Program Execution.......................................................97

Pausing During Program Execution...........................................97

Stopping Program Execution .................................................101

Section 9: Branching and Looping ............................... 103

Simple Branching.......................................................................103

Looping ....................................................................................104

Conditional Branching ................................................................107

Section 10: Program Editing ......................................... 113

Changing the Instruction in a Program Line....................................113

Adding Instructions at the End of a Program ..................................114

Adding Instructions Within a Program...........................................115

Adding Instructions by Replacement.......................................115

Adding Instructions by Branching...........................................116

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Section 11: Multiple Programs ...................................... 120

Storing Another Program ............................................................ 120

Running Another Program........................................................... 122

Part III. Solutions .................................................. 123

Section 12: Real Estate and Lending .............................. 124

Annual Percentage Rate Calculations With Fees............................. 124

Price of a Mortgage Traded at a Discount or Premium.................... 126

Yield of a Mortgage Traded at a Discount or Premium ................... 128

The Rent or Buy Decision ............................................................ 130

Deferred Annuities ..................................................................... 134

Section 13: Investment Analysis .................................... 136

Partial-Year Depreciation............................................................. 136

Straight-Line Depreciation..................................................... 136

Declining-Balance Depreciation ............................................ 139

Sum-of-the-Years-Digits Depreciation ...................................... 141

Full- and Partial-Year Depreciation with Crossover .......................... 144

Excess Depreciation................................................................... 148

Modified Internal Rate of Return................................................... 148

Section 14: Leasing...................................................... 151

Advance Payments..................................................................... 151

Solving For Payment ............................................................ 151

Solving for Yield ................................................................. 154

Advance Payments With Residual ................................................ 156

Solving for Payment............................................................. 156

Solving For Yield................................................................. 158

Section 15: Savings...................................................... 160

Nominal Rate Converted to Effective Rate ..................................... 160

Effective Rate Converted to Nominal Rate ..................................... 161

Nominal Rate Converted to Continuous Effective Rate..................... 162

Section 16: Bonds ........................................................ 163

30/360 Day Basis Bonds........................................................... 163

Annual Coupon Bonds ............................................................... 166

Contents 9

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Appendixes ................................................................ 169

Appendix A: The Automatic Memory Stack ................... 170

Getting Numbers Into the Stack: The Key..............................171

Termination of Digit Entry .....................................................172

Stack Lift.............................................................................172

Rearranging Numbers in the Stack ...............................................172

The key .....................................................................172

The Key.......................................................................172

One-Number Functions and the Stack ...........................................173

Two-Number Functions and the Stack............................................173

Mathematics Functions .........................................................173

Percentage Functions............................................................ 174

Calendar and Financial Functions.................................................175

The LAST X Register and the Key .........................................176

Chain Calculations .....................................................................176

Arithmetic Calculations with Constants ..........................................177

Appendix B: More About L...................................... 179

Appendix C: Error Conditions ...................................... 181

Error 0: Mathematics ..................................................................181

Error 1: Storage Register Overflow ...............................................182

Error 2: Statistics ........................................................................182

Error 3: IRR................................................................................182

Error 4: Memory ........................................................................182

Error 5: Compound Interest..........................................................183

Error 6: Storage Registers............................................................183

Error 7: IRR................................................................................184

Error 8: Calendar.......................................................................184

Error 9: Service..........................................................................184

Pr Error .....................................................................................184

Appendix D: Formulas Used ........................................ 185

Percentage ................................................................................185

Interest ......................................................................................185

Simple Interest.....................................................................185

Compound Interest...............................................................186

Amortization..............................................................................186

Discounted Cash Flow Analysis ....................................................187

Net Present Value ................................................................187

Internal Rate of Return ..........................................................187

Calendar ..................................................................................187

Actual Day Basis .................................................................187

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30/360 Day Basis.............................................................. 187

Bonds ...................................................................................... 188

Depreciation ............................................................................. 189

Straight-Line Depreciation..................................................... 189

Sum-of-the-Years-Digits Depreciation ...................................... 189

Declining-Balance Depreciation ............................................ 190

Modified Internal Rate of Return................................................... 190

Advance Payments..................................................................... 190

Interest Rate Conversions ............................................................ 191

Finite Compounding............................................................ 191

Continuous Compounding.................................................... 191

Statistics ................................................................................... 191

Mean................................................................................ 191

Weighted Mean ................................................................. 191

Linear Estimation................................................................. 191

Standard Deviation ............................................................. 192

Factorial ............................................................................ 192

The Rent or Buy Decision ............................................................ 192

Appendix E: Battery, Warranty, and Service Information 193

Battery ..................................................................................... 193

Low-Power Indication.................................................................. 193

Installing a New Battery ...................................................... 193

Verifying Proper Operation (Self-Tests) .......................................... 194

Warranty.................................................................................. 196

Service..................................................................................... 197

Regulatory Information ............................................................... 199

Temperature Specifications.......................................................... 199

Noise Declaration ..................................................................... 199

Disposal of Waste Equipment by Users in Private Household in the

European Union ........................................................................ 200

Appendix F: United Kingdom Calculations .................... 201

Mortgages................................................................................ 201

Annual Percentage Rate (APR) Calculations ................................... 202

Bond Calculations ..................................................................... 202

Function Key Index...................................................... 203

Programming Key Index .............................................. 206

Subject Index.............................................................. 208

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Making Financial

Calculations Easy

Before you begin to read through this handbook, let’s take a look at how easy

financial calculations can be with your hp 12c. While working through the

examples below, don’t be concerned about learning how to use the calculator;

we’ll cover that thoroughly beginning with Section 1.

Example 1: Suppose you want to ensure that you can finance your daughter’s

college education 14 years from today. You expect that the cost will be about

$6,000 a year ($500 a month) for 4 years. Assume she will withdraw $500 at the

beginning of each month from a savings account. How much would you have to

deposit into the account when she enters college if the account pays 6% annual

interest compounded monthly?

This is an example of a compound interest calculation. All such problems involve at

least three of the following quantities:

z n: the number of compounding periods.

z i: the interest rate per compounding period.

z PV: the present value of a compounded amount.

z PMT: the periodic payment amount.

z FV: the future value of a compounded amount.

In this particular example:

z n is 4 years × 12 periods per year = 48 periods.

z i is 6% per year ÷ 12 periods per year = 0.5% per period.

z PV is the quantity to be calculated — the present value when the financial

transaction begins.

z PMT is $500.

z FV is zero, since by the time your daughter graduates she (hopefully!) will

not need any more money.

To begin, turn the calculator on by pressing the ; key. Then, press the keys

shown in the Keystrokes column below.*

* If you are not familiar with the use of an hp calculator keyboard, refer to the description on

pages 16 and 17.

12 Making Financial Calculations Easy

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Note: A battery symbol (¼) shown in the lower-left corner of the display

when the calculator is on signifies that the available battery power is nearly

exhausted. To install new batteries, refer to Appendix E.

The calendar functions and nearly all of the financial functions take some

time to produce an answer. (This is typically just a few seconds, but the ¼,

!, L, and S functions could require a half-minute or more.) During

these calculations, the word running flashes in the display to let you know

that the calculator is running.

Keystrokes Display

fCLEARHf2 0.00 Clears previous data inside the

calculator and sets display to show

two decimal places.

4gA 48.00 Calculates and stores the number of

compounding periods.

6gC 0.50 Calculates and stores the periodic

interest rate.

500P 500.00 Stores periodic payment amount.

g× 500.00 Sets payment mode to Begin.

$ -21,396.61 Amount required to be deposited.*

Example 2: We now need to determine how to accumulate the required deposit

by the time your daughter enters college 14 years from now. Let’s say that she has

a paid-up $5,000 insurance policy that pays 5.35% annually, compounded

semiannually. How much would it be worth by the time she enters college?

In this example, we need to calculate FV, the future value.

Keystrokes Display

fCLEARG -21,396.61 Clears previous financial data inside

the calculator.

14\2µn 28.00 Calculates and stores the number of

compounding periods.

5.35\2z¼ 2.68 Calculates and stores the periodic

interest rate.

5000Þ$ -5,000.00 Stores the present value of the

policy.

M 10,470.85 Value of policy in 14 years.

* Don’t be concerned now about the minus sign in the display. That and other details will be

explained in Section 3.

Making Financial Calculations Easy 13

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Example 3: The preceding example showed that the insurance policy will

provide about half the required amount. An additional amount must be set aside to

provide the balance (21,396.61 – 10,470.85 = 10,925.76). Suppose you make

monthly payments, beginning at the end of next month, into an account that pays

6% annually, compounded monthly. What payment amount would be required in

order to accumulate $10,925.75 in the 14 years remaining?

Keystrokes Display

fCLEARG 10,470.85 Clears previous financial data

inside the calculator.

14gA 168.00 Calculates and stores the number of

compounding periods.

6gC 0.50 Calculates and stores the periodic

interest rate.

10925.76M 10.925.76 Stores the future value required.

gÂ 10.925.76 Sets payment mode to End.

P –41.65 Monthly payment required.

Example 4: Suppose you cannot find a bank that currently offers an account

with 6% annual interest compounded monthly, but you can afford to make $45.00

monthly payments. What is the minimum interest rate that will enable you to

accumulate the required amount?

In this problem, we do not need to clear the previous financial data inside the

calculator, since most of it is unchanged from the preceding example.

Keystrokes Display

45ÞP –45.00 Stores payment amount.

¼ 0.42 Periodic interest rate.

12§ 5.01 Annual interest rate.

This is only a small sampling of the many financial calculations that can now be

done easily with your hp 12c. To begin learning about this powerful financial tool,

just turn the page.

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Part I

Problem Solving

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Section 1

Getting Started

Power On and Off

To begin using your hp 12c, press the ; key*. Pressing ; again turns the

calculator off. If not manually turned off, the calculator will turn off automatically 8

to 17 minutes after it was last used.

Low-Power Indication

A battery symbol (¼) shown in the upper-left corner of the display when the

calculator is on signifies that the available battery power is nearly exhausted. To

replace the batteries, refer to Appendix E.

The Keyboard

Many keys on the hp 12c perform two or even three functions. The primary

function of a key is indicated by the characters printed in white on the upper face

of the key. The alternate function(s) of a key are indicated by the characters

printed in gold above the key and the characters printed in blue on the lower face

of the key. These alternate functions are specified by pressing the appropriate

prefix key before the function key:

z To specify the alternate function printed in

g

old

above a key, press the gold prefix key (f), then

press the function key.

z To specify the primary function printed on the uppe

r

face of a key, press the key alone.

z To specify the alternate function printed in blue on the

lower face of a key, press the blue prefix key (g),

then press the function key.

* Note that the ; key is lower than the other keys to help prevent its being pressed

inadvertently.

Section 1: Getting Started 17

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Throughout this handbook, references to the operation of an alternate function

appear as only the function name in a box (for example, “The L function …”).

References to the selection of an alternate function appear preceded by the

appropriate prefix key (for example, “Pressing fL …”). References to the

functions shown on the keyboard in gold under the bracket labeled “CLEAR”

appear throughout this handbook preceded by the word “CLEAR” (for example,

“The CLEARH function …” or “Pressing fCLEARH …”).

If you press the f or g prefix key mistakenly, you can cancel it by pressing

fCLEARX. This can also be pressed to cancel the ?, :, and i keys.

(These keys are “prefix” keys in the sense that other keys must be pressed after

them in order to execute the corresponding function.) Since the X key is also

used to display the mantissa (all 10 digits) of a displayed number, the mantissa of

the number in the display will appear for a moment after the X key is released.

Pressing the f or g prefix key turns on the corresponding status indicator — f

or g — in the display. Each indicator turns off when you press a function key

(executing an alternate function of that key), another prefix key, or fCLEARX.

Keying in Numbers

To key a number into the calculator, press the digit keys in sequence, just as if you

were writing the number on paper. A decimal point must be keyed in (using the

decimal point key) if it is part of the number unless it appears to the right of the last

digit.

Digit Separators

As a number is keyed in, each group of three digits to the left of the decimal point

is automatically separated in the display. When the calculator is first turned on

after coming from the factory — or after Continuous Memory is reset — the

decimal point in displayed numbers is a dot, and the separator between each

group of three digits is a comma. If you wish, you can set the calculator to display

a comma for the decimal point and a dot for the three-digit separator. To do so,

turn the calculator off, then press and hold down the . key while you press ;.

Doing so again sets the calculator to use the original digit separators in the

display.

Negative Numbers

To make a displayed number negative — either one that has just been keyed in or

one that has resulted from a calculation — simply press Þ (change sign) . When

the display shows a negative number — that is, the number is preceded by a

minus sign — pressing Þ removes the minus sign from the display, making the

number positive.

18 Section 1: Getting Started

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Keying in Large Numbers

Since the display cannot show more than 10 digits of a number, numbers greater

than 9,999,999,999 cannot be entered into the display by keying in all the digits

in the number. However, such numbers can be easily entered into the display if the

number is expressed in a mathematical shorthand called “scientific notation.” To

convert a number into scientific notation, move the decimal point until there is only

one digit (a nonzero digit) to its left. The resulting number is called the “mantissa”

of the original number, and the number of decimal places you moved the decimal

point is called the “exponent” of the original number. If you moved the decimal

point to the left, the exponent is positive; if you moved the decimal point to the

right (this would occur for numbers less than one), the exponent is negative. To key

the number into the display, simply key in the mantissa, press Æ (enter exponent),

then key in the exponent. If the exponent is negative, press Þ after pressing

Æ.

For example, to key in $1,781,400,000,000, we move the decimal point 12

places to the left, giving a mantissa of 1.7814 and an exponent of 12:

Keystrokes Display

1.7814Æ12 1.7814 12 1,781,400,000,000 entered in

scientific notation.

Numbers entered in scientific notation can be used in calculations just like any

other number.

The CLEAR Keys

Clearing a register or the display replaces the number in it with zero. Clearing

program memory replaces the instructions there with gi00. There are several

clearing operations on the hp 12c, as shown in the table below:

Key(s) Clears:

O Display and X-register.

fCLEAR² Statistics registers (R1 through R6), stack registers, and

display.

fCLEARÎ Program memory (only when pressed in Program mode).

fCLEARG Financial registers.

fCLEARH Data storage registers, financial registers, stack and LAST X

registers, and display.

Section 1: Getting Started 19

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Simple Arithmetic Calculations

Any simple arithmetic calculation involves two numbers and an operation —

addition, subtraction, multiplication, or division. To do such a calculation on your

hp 12c, you first tell the calculator the two numbers, then tell the calculator the

operation to be performed. The answer is calculated when the operation key

(+,-,§, or z) is pressed.

The two numbers should be keyed into the calculator in the order they would

appear if the calculation were written down on paper left-to-right. After keying in

the first number, press the \ key to tell the calculator that you have completed

entering the number. Pressing \ separates the second number to be entered

from the first number already entered.

In summary, to perform an arithmetic operation:

1. Key in the first number.

2. Press \ to separate the second number from the first.

3. Key in the second number.

4. Press +,-,§, or z to perform the desired operation.

For example to calculate 13 ÷ 2, proceed as follows:

Keystrokes Display

13 13. Keys the first number into the

calculator.

\ 13.00 Pressing \ separates the second

number from the first.

2 2. Keys the second number into the

calculator.

z 6.50 Pressing the operation key calculates

the answer.

Notice that after you pressed \, two zeroes appeared following the decimal

point. This is nothing magical: the calculator’s display is currently set to show two

decimal places of every number that has been entered or calculated. Before you

pressed \, the calculator had no way of knowing that you had completed

entering the number, and so displayed only the digits you had keyed in. Pressing

\ tells the calculator that you have completed entering the number: it terminates

digit entry. You need not press \ after keying in the second number because

the +,-,§ and z keys also terminate digit entry. (In fact, all keys terminate

digit entry except for digit entry keys — digit keys, ., Þ, and Æ — and

prefix keys — f, g, ?, :, and (.)

20 Section 1: Getting Started

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Chain Calculations

Whenever the answer has just been calculated and is therefore in the display, you

can perform another operation with this number by simply keying in the second

number and then pressing the operation key: you need not press \ to separate

the second number from the first. This is because when a number is keyed in after

a function key (such as +,-,§, z, etc.) is pressed, the result of that prior

calculation is stored inside the calculator — just as when the \ key is pressed.

The only time you must press the \ key to separate two numbers is when you

are keying them both in, one immediately following the other.

The hp 12c is designed so that each time you press a function key in RPN mode,

the calculator performs the operation then — not later — so that you see the results

of all intermediate calculations, as well as the “bottom line.”

Example: Suppose you’ve written three checks without updating your checkbook,

and you’ve just deposited your paycheck for $1,053.00 into your checking

account. If your latest balance was $58.33 and the checks were written for

$22.95, $13.70, and $10.14, what is the new balance?

Solution: When written down on paper, this problem would read

58.33 – 22.95 – 13.70 – 10.14 + 1053

Keystrokes Display

58.33 58.33 Keys the first number.

\ 58.33 Pressing \ separates the second

number from the first.

22.95 22.95 Keys in the second number.

- 35.38 Pressing - subtracts the second

number from the first. The calculator

displays the result of this calculation,

which is the balance after subtracting

the first check.

13.70 13.70 Keys in the next number. Since a

calculation has just been performed,

do not press \; the next number

entered (13.70) is automatically

separated from the one previously in

the display (35.38).

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Keystrokes Display

- 21.68 Pressing - subtracts the number just

entered from the number previously in

the display. The calculator displays the

result of this calculation, which is the

balance after subtracting the second

check.

10.14- 11.54 Keys in the next number and subtracts

it from the previous balance. The new

balance appears in the display. (It’s

getting rather low!)

1053+ 1,064.54 Keys in the next number — the

paycheck deposited — and adds it to

the previous balance. The new,

current balance appears in the

display.

The preceding example demonstrates how the hp 12c calculates just as you would

using pencil and paper (except a lot faster!):

Let’s see this happening in a different type of calculation — one that involves

multiplying groups of two numbers and then adding the results. (This is the type of

calculation that would be required to total up an invoice consisting of several items

with different quantities and different prices.)

For example, consider the calculation of (3 × 4) + (5 × 6). If you were doing this

on paper, you would first do the multiplication in the first parentheses, then the

multiplication in the second parentheses, and finally add the results of the two

multiplications:

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Your hp 12c calculates the answer in just the same way:

Keystrokes Display

3\4§ 12.00 Step 1: Multiply the numbers in the

first parentheses.

5\6§ 30.00 Step 2: Multiply the numbers in the

second parentheses.

+ 42.00 Step 3: Add the results of the two

multiplications.

Notice that before doing step 2, you did not need to store or write down the result

of step 1: it was stored inside the calculator automatically. And after you keyed in

the 5 and the 6 in step 2, the calculator was holding two numbers (12 and 5)

inside for you, in addition to the 6 in the display. (The hp 12c can hold a total of

three numbers inside, in addition to the number in the display.) After step 2, the

calculator was still holding the 12 inside for you, in addition to the 30 in the

display. You can see that the calculator holds the number for you, just as you

would have them written on paper, and then calculates with them at the proper

time, just as you would yourself.* But with the hp 12c, you don’t need to write

down the results of an intermediate calculation, and you don’t even need to

manually store it and recall it later.

By the way, notice that in step 2 you needed to press \ again. This is simply

because you were again keying in two numbers immediately following each other,

without performing a calculation in between.

To check your understanding of how to calculate with your hp 12c, try the

following problems yourself. Although these problems are relatively simple, more

complicated problems can be solved using the same basic steps. If you have

difficulty obtaining the answers shown, review the last few pages.

00.77)65()43(

=

+

×

+

25.0

)3814(

)1427( =

+

−

13.0

21163

5=

++

* Although you don’t need to know just how these numbers are stored and brought back at just

the right time, if you’re interested you can read all about it in Appendix A. By gaining a more

complete understanding of the calculator’s operation, you’ll use it more efficiently and

confidently, yielding a better return on the investment in your hp 12c.

Section 1: Getting Started 23

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Storage Registers

Numbers (data) in the hp 12c are stored in memories called “storage registers” or

simply “registers.” (The singular term “ memory” is sometimes used in this

handbook to refer to the entire collection of storage registers.) Four special

registers are used for storing numbers during calculations (these “stack registers”

are described in Appendix A), and another (called the “LAST X” register) is used

for storing the number last in the display before an operation is performed. In

addition to these registers into which numbers are stored automatically, up to 20

“data storage” registers are available for manual storage of numbers. These data

storage registers are designated R0 through R9 and R.0 through R.9. Fewer registers

are available for data storage if a program has been stored in the calculator (since

the program is stored in some of those 20 registers), but a minimum of 7 registers

is always available. Still other storage registers — referred to as the “financial

registers” — are reserved for numbers used in financial calculations.

Storing and Recalling Numbers

To store the number from the display into a data storage register:

1. Press ? (store).

2. Key in the register number: 0 through 9 for registers R0 through R9, or .0

through .9 for registers R.0 through R.9.

Similarly, to recall a number from a storage register into the display, press :

(recall), then key in the register number. This copies the number from the storage

register into the display; the number remains unaltered in the storage register.

Furthermore, when this is done, the number previously in the display is

automatically held inside the calculator for a subsequent calculation, just as the

number in the display is held when you key in another number.

Example: Before you leave to call on a customer interested in your personal

computer, you store the cost of the computer ($3,250) and also the cost of a

printer ($2,500) in data storage registers. Later, the customer decides to buy six

computers and one printer. You recall the cost of the computer, multiply by the

quantity ordered, and then recall and add the cost of the printer to get the total

invoice.

Keystrokes Display

3250?1 3,250.00 Stores the cost of the computer in R1.

2500?2 2,500.00 Stores the cost of the printer in R2.

; Turns the calculator off.

24 Section 1: Getting Started

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Later that same day …

Keystrokes Display

; 2,500.00 Turns the calculator back on.

:1 3,250.00 Recalls the cost of the computer to the

display.

6§ 19,500.00 Multiplies the quantity ordered to get

the cost of the computers.

:2 2,500.00 Recalls the cost of the printer to the

display.

+ 22,000.00 Total invoice.

Clearing Storage Registers

To clear a single storage register — that is, to replace the number in it with

zero — merely store zero into it. You need not clear a storage register before

storing data into it; the storing operation automatically clears the register before

the data is stored.

To clear all storage registers at once — including the financial registers, the stack

registers, and the LAST X register — press fCLEARH.* This also clears the

display.

All storage registers are also cleared when Continuous Memory is reset (as

described on page 70).

Storage Register Arithmetic

Suppose you wanted to perform an arithmetic operation with the number in the

display and the number in a storage register, then store the result back into the

same register without altering the number in the display. The hp 12c enables you

to do all this in a single operation:

1. Press ?.

2. Press +, -, §, or z to specify the desired operation.

3. Key in the register number.

When storage register arithmetic is performed, the new number in the register is

determined according to the following rule:

* CLEARH is not programmable.

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Storage register arithmetic is possible with only registers R0 through R4.

Example: In the example on page 20, we updated the balance in your

checkbook. Let’s suppose that because data is stored indefinitely in your

calculator’s Continuous Memory, you keep track of your checking account balance

in the calculator. You could use storage register arithmetic to quickly update the

balance after depositing or writing checks.

Keystrokes Display

58.33?0 58.33 Stores the current balance in register

R0.

22.95?-0 22.95 Subtracts the first check from the

balance in R0. Note that the display

continues to show the amount

subtracted; the answer is placed only

in R0.

13.70?-0 13.70 Subtracts the second check.

10.14?-0 10.14 Subtracts the third check.

1053?+0 1,053.00 Adds the deposit.

:0 1,064.54 Recalls the number in R0 to check the

new balance.

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Section 2

Percentage and Calendar

Functions

Percentage Functions

The hp 12c includes three keys for solving percentage problems: b, à, and Z.

You don’t need to convert percentages to their decimal equivalents; this is done

automatically when you press any of these keys. Thus, 4% need not be changed to

0.04; you key it in the way you see and say it: 4b.

Percentages

To find the amount corresponding to a percentage of a number:

1. Key in the base number.

2. Press \.

3. Key in the percentage.

4. Press b.

For example, to find 14% of $300:

Keystrokes Display

300 300. Keys in the base number.

\ 300.00 Pressing \ separates the next

number entered from the first number,

just as when an ordinary arithmetic

calculation is performed.

14 14. Keys in the percentage.

b 42.00 Calculates the amount.

If the base number is already in the display as a result of a previous calculation,

you should not press \ before keying in the percentage — just as in a chain

arithmetic calculation.

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Net Amount

A net amount — that is, the base amount plus or minus the percentage amount —

can be calculated easily with your hp 12c, since the calculator holds the base

amount inside after you calculate a percentage amount. To calculate a net amount,

simply calculate the percentage amount, then press = or -.

Example: You’re buying a new car that lists for $13,250. The dealer offers you

a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging

you, then find the total cost to you, including tax.

Keystrokes Display

13250\ 13,250.00 Keys in the base amount and

separates it from the percentage.

8b 1,060.00 Amount of discount.

- 12,190.00 Base amount less discount.

6b 731.40 Amount of tax (on $12,190).

= 12,921.40 Total cost: base amount less discount

plus tax.

Percent Difference

To find the percent difference between two numbers:

1. Key in the base number.

2. Press \ to separate the other number from the base number.

3. Key in the other number.

4. Press à.

If the other number is greater than the base number, the percent difference will be

positive. If the other number is less than the base number, the percent difference

will be negative. Therefore, a positive answer indicates an increase, while a

negative answer indicates a decrease.

If you are calculating a percent difference over time, the base number is typically

the amount occurring first.

Example: Yesterday your stock fell from 581/2 to 531/4 per share. What is the

percent change?

Keystrokes Display

58.5\ 58.50 Keys in the base number and

separates it from the other number.

53.25 53.25 Keys in the other number.

à –8.97 Nearly a 9% decrease.

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The à key can be used for calculations of the percent difference between a

wholesale cost and a retail cost. If the base number entered is the wholesale cost,

the percent difference is called the markup; if the base number entered is the retail

cost, the percent difference is called the margin. Examples of markup and margin

calculations are included in the hp 12c Solutions Handbook.

Percent of Total

To calculate what percentage one number is of another:

1. Calculate the total amount by adding the individual amounts, just as in a

chain arithmetic calculation.

2. Key in the number whose percentage equivalent you wish to find.

3. Press Z.

Example: Last month, your company posted sales of $3.92 million in the U.S.,

$2.36 million in Europe, and $1.67 million in the rest of the world. What

percentage of the total sales occurred in Europe?

Keystrokes Display

3.92\ 3.92 Keys in the first number and separates

it from the second.

2.36+ 6.28 Adds the second number.

1.67+ 7.95 Adds the third number to get the total.

2.36 2.36 Keys in 2.36 to find what percentage

it is of the number in the display.

Z 29.69 Europe had nearly 30% of the total

sales.

The hp 12c holds the total amount inside after a percent of total is calculated.

Therefore, to calculate what percentage another amount is of the total:

1. Clear the display by pressing O.

2. Key in that amount.

3. Press Z again.

For example, to calculate what percent of the total sales in the preceding example

occurred in the U.S. and what percent occurred in the rest of the world:

Keystrokes Display

O3.92Z 49.31 The U.S. had about 49% of the total

sales.

O1.67 Z 21.01 The rest of the world had about 21%

of the total sales.

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To find what percentage a number is of a total, when you already know the total

number:

1. Key in the total number.

2. Press \ to separate the other number from the total number.

3. Key in the number whose percentage equivalent you wish to find.

4. Press Z.

For example, if you already knew in the preceding example that the total sales

were $7.95 million and you wanted to find what percentage of that total occurred

in Europe:

Keystrokes Display

7.95\ 7.95 Keys in the total amount and separates

it from the next number.

2.36 2.36 Keys in 2.36 to find what percentage

it is of the number in the display.

Z 29.69 Europe had nearly 30% of the total

sales.

Calendar Functions

The calendar functions provided by the hp 12c — D and Ò — can handle

dates from October 15, 1582 through November 25, 4046.

Date Format

For each of the calendar functions — and also for bond calculations (E and

S) — the calculator uses one of two date formats. The date format is used to

interpret dates when they are keyed into the calculator as well as for displaying

dates.

Month-Day-Year. To set the date format to month-day-year, press gÕ. To

key in a date with this format in effect:

1. Key in the one or two digits of the month.

2. Press the decimal point key (.).

3. Key in the two digits of the day.

4. Key in the four digits of the year.

Dates are displayed in the same format.

For example, to key in April 7, 2004:

Keystrokes Display

4.072004 4.072004

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Day-Month-Year. To set the date format to day-month-year, press gÔ. To

key in a date with this format in effect:

1. Key in the one or two digits of the day.

2. Press the decimal point key (.).

3. Key in the two digits of the month.

4. Key in the four digits of the year.

For example, to key in 7 April, 2004:

Keystrokes Display

7.042004 7.042004

When the date format is set to day-month-year, the D.MY status indicator in the

display is lit. If D.MY is not lit, the date format is set to month-day-year.

The date format remains set to what you last specified until you change it; it is not

reset each time the calculator is turned on. However, if Continuous Memory is reset,

the date format is set to month-day-year.

Future or Past Dates

To determine the date and day that is a given number of days from a given date:

1. Key in the given date and press \.

2. Key in the number of days.

3. If the other date is in the past, press Þ.

4. Press gD.

The answer calculated by the D function is displayed in a special format. The

numbers of the month, day, and year (or day, month, and year) are separated by

digit separators, and the digit at the right of the displayed answer indicates the

day of the week: 1 for Monday through 7 for Sunday.*

Example: If you purchased a 120-day option on a piece of land on 14 May

2004, what would be the expiration date? Assume that you normally express

dates in the day-month-year format.

Keystrokes Display

gÔ 7.04 Sets date format to day-month-year.

(Display shown assumes date

remains from preceding example.

The full date is not now displayed

because the display format is set to

show only two decimal places, as

described in Section 5.)

* The day of the week indicated by the D function may differ from that recorded in history

for dates when the Julian calendar was in use. The Julian calendar was standard in England

and its colonies until September 14, 1752, when they switched to the Gregorian calendar.

Other countries adopted the Gregorian calendar at various times.

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Keystrokes Display

14.052004\ 14.05 Keys in date and separates it from

number of days to be entered.

120gD 11,09,2004 6 The expiration date is 11 September

2004, a Saturday.

When D is executed as an instruction in a running program, the calculator

pauses for about 1 second to display the result, then resumes program execution.

Number of Days Between Dates

To calculate the number of days between two given dates:

1. Key in the earlier date and press \.

2. Key in the later date and press gÒ.

The answer shown in the display is the actual number of days between the two

dates, including leap days (the extra days occurring in leap years), if any. In

addition, the hp 12c also calculates the number of days between the two dates on

the basis of a 30-day month. This answer is held inside the calculator; to display it,

press ~. Pressing ~ again will return the original answer to the display.

Example: Simple interest calculations can be done using either the actual number

of days or the number of days counted on the basis of a 30-day month. What

would be the number of days counted each way, to be used in calculating the

simple interest accruing from June 3, 2004 to October 14, 2005? Assume that

you normally express dates in the month-day-year format.

Keystrokes Display

gÕ 11.09 Sets date format to month-day-year.

(Display shown assumes date remains

from preceding example.)

6.032004\ 6.03 Keys in earlier date and separates it

from the later date.

10.142005gÒ 498.00 Keys in later date. Display shows

actual number of days.

~ 491.00 Number of days counted on the basis

of a 30-day month.

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Section 3

Basic Financial Functions

The Financial Registers

In addition to the data storage registers discussed on page 23, the hp 12c has five

special registers in which numbers are stored for financial calculations. These

registers are designated n, i, PV, PMT, and FV. The first five keys on the top row of

the calculator are used to store a number from the display into the corresponding

register, to calculate the corresponding financial value and store the result into the

corresponding register, or to display the number stored in the corresponding

register.*

Storing Numbers Into the Financial Registers

To store a number into a financial register, key the number into the display, then

press the corresponding key (n, ¼, $, P, or M).

Displaying Numbers in the Financial Registers

To display a number stored in a financial register, press : followed by the

corresponding key.†

* Which operation is performed when one of these keys is pressed depends upon the last

preceding operation performed: If a number was just stored into a financial register (using

n, ¼, $, P, M, A, or C), pressing one of these five keys calculates the

corresponding value and stores it into the corresponding register; otherwise pressing one of

these five keys merely stores the number from the display into the corresponding register.

† It’s good practice to press the corresponding key twice after :, since often you may want

to calculate a financial value right after displaying another financial value. As indicated in

the preceding footnote, if you wanted to display FV and then calculate PV, for example, you

should press :MM$. If you didn’t press M the second time, pressing $ would

store FV in the PV register rather than calculating PV, and to calculate PV you would have to

press $ again.

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Clearing the Financial Registers

Every financial function uses numbers stored in several of the financial registers.

Before beginning a new financial calculation, it is good practice to clear all of the

financial registers by pressing fCLEARG. Frequently, however, you may want

to repeat a calculation after changing a number in only one of the financial

registers. To do so, do not press fCLEARG; instead, simply store the new

number in the register. The numbers in the other financial registers remain

unchanged.

The financial registers are also cleared when you press fCLEARH and when

Continuous Memory is reset (as described on page 70).

Simple Interest Calculations

The hp 12c simultaneously calculates simple interest on both a 360-day basis and

a 365-day basis. You can display either one, as described below. Furthermore,

with the accrued interest in the display, you can calculate the total amount

(principal plus accrued interest) by pressing +.

1. Key in or calculate the number of days, then press n.

2. Key in the annual interest rate, then press ¼.

3. Key in the principal amount, then press Þ$.*

4. Press fÏ to calculate and display the interest accrued on a 360-day

basis.

5. If you want to display the interest accrued on a 365-day basis, press

d~.

6. Press + to calculate the total of the principal and the accrued interest now

in the display.

The quantities n, i, and PV can be entered in any order.

Example 1: Your good friend needs a loan to start his latest enterprise and has

requested that you lend him $450 for 60 days. You lend him the money at 7%

simple interest, to be calculated on a 360-day basis. What is the amount of

accrued interest he will owe you in 60 days, and what is the total amount owed?

Keystrokes Display

60n 60.00 Stores the number of days.

* Pressing the $ key stores the principal amount in the PV register, which then contains the

present value of the amount on which interest will accrue. The Þ key is pressed first to

change the sign of the principal amount before storing it in the PV register. This is required by

the cash flow sign convention, which is applicable primarily to compound interest

calculations.

34 Section 3: Basic Financial Functions

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Keystrokes Display

7¼ 7.00 Stores the annual interest rate.

450Þ$ –450.00 Stores the principal.

fÏ 5.25 Accrued interest, 360-day basis.

+ 455.25 Total amount: principal plus accrued

interest.

Example 2: Your friend agrees to the 7% interest on the loan from the preceding

example, but asks that you compute it on a 365-day basis rather than a 360-day

basis. What is the amount of accrued interest he will owe you in 60 days, and

what is the total amount owed?

Keystrokes Display

60n

7¼

450Þ$

60.00

7.00

–450.00

If you have not altered the numbers in

the n, i, and PV registers since the

preceding example, you may skip

these keystrokes.

fÏd~ 5.18 Accrued interest, 365-day basis.

+ 455.18 Total amount: principal plus accrued

interest.

Financial Calculations and the Cash Flow Diagram

The concepts and examples presented in this section are representative of a wide

range of financial calculations. If your specific problem does not appear to be

illustrated in the pages that follow, don’t assume that the calculator is not capable

of solving it. Every financial calculation involves certain basic elements; but the

terminology used to refer to these elements typically differs among the various

segments of the business and financial communities. All you need to do is identify

the basic elements in your problem, and then structure the problem so that it will

be readily apparent what quantities you need to tell the calculator and what

quantity you want to solve for.

An invaluable aid for using your calculator in a financial calculation is the cash

flow diagram. This is simply a pictorial representation of the timing and direction

of financial transactions, labeled in terms that correspond to keys on the calculator.

The diagram begins with a horizontal line, called a time line. It represents the

duration of a financial problem, and is divided into compounding periods. For

example, a financial problem that transpires over 6 months with monthly

compounding would be diagrammed like this:

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The exchange of money in a problem is depicted by vertical arrows. Money you

receive is represented by an arrow pointing up from the point in the time line when

the transaction occurs; money you pay out is represented by an arrow pointing

down.

Suppose you deposited (paid out) $1,000 into an account that pays 6% annual

interest and is compounded monthly, and you subsequently deposited an

additional $50 at the end of each month for the next 2 years. The cash flow

diagram describing the problem would look like this:

The arrow pointing up at the right of the diagram indicates that money is received

at the end of the transaction. Every completed cash flow diagram must include at

least one cash flow in each direction. Note that cash flows corresponding to the

accrual of interest are not represented by arrows in the cash flow diagram.

The quantities in the problem that correspond to the first five keys on the top row of

the keyboard are now readily apparent from the cash flow diagram.

z n is the number of compounding periods. This quantity can be expressed in

years, months, days, or any other time unit, as long as the interest rate is

expressed in terms of the same basic compounding period. In the problem

illustrated in the cash flow diagram above, n = 2 × 12.

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The form in which n is entered determines whether or not the calculator

performs financial calculations in Odd-Period mode (as described on pages

50 through 53). If n is a noninteger (that is, there is at least one nonzero

digit to the right of the decimal point), calculations of i, PV, PMT, and FV are

performed in Odd-Period mode.

z i is the interest rate per compounding period. The interest rate shown in the

cash flow diagram and entered into the calculator is determined by dividing

the annual interest rate by the number of compounding periods. In the

problem illustrated above, i = 6% ÷ 12.

z PV — the present value — is the initial cash flow or the present value of a

series of future cash flows. In the problem illustrated above, PV is the $1,000

initial deposit.

z PMT is the period payment. In the problem illustrated above PMT is the $50

deposited each month. When all payments are equal, they are referred to as

annuities. (Problems involving equal payments are described in this section

under Compound Interest Calculations; problems involving unequal

payments can be handled as described in under Discounted Cash Flow

Analysis: NPV and IRR. Procedures for calculating the balance in a savings

account after a series of irregular and/or unequal deposits are included in

the hp 12c Solutions Handbook.)

z FV — the future value — is the final cash flow or the compounded value of a

series of prior cash flows. In the particular problem illustrated above, FV is

unknown (but can be calculated).

Solving the problem is now basically a matter of keying in the quantities identified

in the cash flow diagram using the corresponding keys, and then calculating the

unknown quantity by pressing the corresponding key. In the particular problem

illustrated in the cash flow diagram above, FV is the unknown quantity; but in other

problems, as we shall see later, n, i, PV, or PMT could be the unknown quantity.

Likewise, in the particular problem illustrated above there are four known

quantities that must be entered into the calculator before solving for the unknown

quantity; but in other problems only three quantities may be known — which must

always include n or i.

The Cash Flow Sign Convention

When entering the PV, PMT, and FV cash flows, the quantities must be keyed into

the calculator with the proper sign, + (plus) or – (minus), in accordance with …

The Cash Flow Sign Convention: Money received (arrow pointing up)

is entered or displayed as a positive value (+). Money paid out (arrow

pointing down) is entered or displayed as a negative value (–).

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The Payment Mode

One more bit of information must be specified before you can solve a problem

involving periodic payments. Such payments can be made either at the beginning

of a compounding period (payments in advance, or annuities due) or at the end of

the period (payments in arrears, or ordinary annuities). Calculations involving

payments in advance yield different results than calculations involving payments in

arrears. Illustrated below are portions of cash flow diagrams showing payments in

advance (Begin) and payments in arrears (End). In the problem illustrated in the

cash flow diagram above, payments are made in arrears.

Regardless of whether payments are made in advance or in arrears, the number of

payments must be the same as the number of compounding periods.

To specify the payment mode:

z Press g× if payments are made at the beginning of the compounding

periods.

z Press gÂ if payments are made at the end of the compounding periods.

The BEGIN status indicator is lit when the payment mode is set to Begin. If BEGIN

is not lit, the payment mode is set to End.

The payment mode remains set to what you last specified until you change it; it is

not reset each time the calculator is turned on. However, if Continuous Memory is

reset, the payment mode will be set to End.

Generalized Cash Flow Diagrams

Examples of various kinds of financial calculations, together with the applicable

cash flow diagrams, appear under Compound Interest Calculations later in this

section. If your particular problem does not match any of those shown, you can

solve it nevertheless by first drawing a cash flow diagram, then keying the

quantities identified in the diagram into the corresponding registers. Remember

always to observe the sign convention when keying in PV, PMT, and FV.

The terminology used for describing financial problems varies among the different

segments of the business and financial communities. Nevertheless, most problems

involving compound interest can be solved by drawing a cash flow diagram in

one of the following basic forms. Listed below each form are some of the problems

to which that diagram applies.

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Compound Interest Calculations

Specifying the Number of Compounding Periods and the Periodic

Interest Rate

Interest rates are usually quoted at the annual rate (also called the nominal rate):

that is, the interest rate per year. However, in compound interest problems, the

interest rate entered into i must always be expressed in terms of the basic

compounding period, which may be years, months, days, or any other time unit.

For example, if a problem involves 6% annual interest compounded quarterly for 5

years, n — the number of quarters — would be 5 × 4 = 20 and i — the interest

rate per quarter — would be 6% ÷ 4 = 1.5%. If the interest were instead

compounded monthly, n would be 5 × 12 = 60 and i would be 6% ÷ 12 = 0.5%.

If you use the calculator to multiply the number of years by the number of

compounding periods per year, pressing n then stores the result into n. The same

is true for i. Values of n and i are calculated and stored like this in Example 2 on

page 47.

If interest is compounded monthly, you can use a shortcut provided on the

calculator to calculate and store n and i:

z To calculate and store n, key the number of years into the display, then press

gA.

z To calculate and store i, key the annual rate into the display, then press

gC.

Note that these keys not only multiply or divide the displayed number by 12; they

also automatically store the result in the corresponding register, so you need not

press the n or ¼ key next. The A and C keys are used in Example 1 on

page 46.

Calculating the Number of Payments or Compounding Periods

1. Press fCLEARG to clear the financial registers.

2. Enter the periodic interest rate, using ¼ or C.

3. Enter at least two of the following values:

z Present value, using $.

z Payment amount, using P.

z Future value, using M.

Note: Remember to observe

the cash flow sign convention.

4. If a PMT was entered, press g× or gÂ to set the payment mode.

5. Press n to calculate the number of payments or periods.

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If the answer calculated is not an integer (that is, there would be nonzero digits to

the right of the decimal point), the calculator rounds the answer up to the next

higher integer before storing it in the n register and displaying it.* For example, if

n were calculated as 318.15, 319.00 would be the displayed answer.

n is rounded up by the calculator to show the total number of payments needed:

n–1 equal, full payments, and one final, smaller payment. The calculator does not

automatically adjust the values in the other financial registers to reflect n equal

payments; rather, it allows you to choose which, if any, of the values to adjust.†

Therefore, if you want to know the value of the final payment (with which you can

calculate a balloon payment) or desire to know the payment value for n equal

payments, you will need to press one of the other financial keys, as shown in the

following two examples.

Example 1: You’re planning to build a log cabin on your vacation property.

Your rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325

payments at the end of each month, how many payments will be required to pay

off the loan, and how many years will this take?

Keystrokes Display

fCLEARG

10.5gC

0.88

Calculates and stores i.

35000$ 35,000.00 Stores PV.

325ÞP –325.00 Stores PMT (with minus sign for cash

paid out).

gÂ –325.00 Sets the payment mode to End.

n 328.00 Number of payments required.

* The calculator will round n down to the next lower integer if the fractional portion of n is less

than 0.005.

† After calculating n, pressing ¼, $, P, or M will recalculate the value in the

corresponding financial register.

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Keystrokes Display

12z 27.33 Twenty-seven years and four months.

Because the calculator rounds the calculated value of n up to the next higher

integer, in the preceding example it is likely that — while 328 payments will be

required to pay off the loan — only 327 full payments of $325 will be required,

the next and final payment being less than $325. You can calculate the final,

fractional, 328th payment as follows:

Keystrokes Display

328n 328.00 Stores total number of payments.*

M 181.89 Calculates FV — which equals the

overpayment if 328 full payments

were made.

:P –325.00 Recalls payment amount.

+ –143.11 Final, fractional payment.

Alternatively, you could make the fractional payment together with the 327th

payment. (Doing so will result in a somewhat smaller total of all payments, since

you will not have to pay interest during the 328th payment period.) You can

calculate this final, larger, 327th payment (essentially a balloon payment) as

follows:

Keystrokes Display

327n 327.00 Stores number of full payments.

M –141.87 Calculates FV — which is the balance

remaining after 327 full payments.

:P –325.00 Recalls payment amount.

+ –466.87 Final, balloon payment.

Instead of having a fractional (or balloon) payment at the end of the loan, you

might wish to make 327 or 328 equal payments. Refer to “Calculating the

Payment Amount” on page 46 for a complete description of this procedure.

* You could skip this step, since 328 is already stored in the n register. If you do so, however,

you will need to press M twice in the next step (for the reason discussed in the first footnote

on page 32; you would not have to press M twice if you had not pressed 12z after w in

the example above.) We choose to show this and the following example in a parallel format

so that the procedure is easy to remember: the number you key is the number of the final

payment — either the fractional payment or the balloon payment — whose amount is to be

calculated.

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Example 2: You’re opening a savings account today (the middle of the month)

with a $775 deposit. The account pays 61/4% interest compounded semimonthly.

If you make semimonthly deposits of $50 beginning next month, how long will it

take for your account to reach $4000?

Keystrokes Display

fCLEARG

6.25\24z¼

0.26

Calculates and stores i.

775Þ$ –775.00 Stores PV (with minus sign for cash

paid out).

50ÞP –50.00 Stores PMT (with minus sign for cash

paid out).

4000M 4,000.00 Stores FV.

gÂ 4,000.00 Sets the payment mode to End.

n 58.00 Number of semimonthly deposits.

2z 29.00 Number of months.

As in Example 1, it is likely that only 57 full deposits will be required, the next and

final deposit being less than $50. You can calculate this final, fractional, 58th

deposit as in Example 1, except that for this example you must subtract the original

FV. (In Example 1, the original FV was zero.) The procedure is as follows:

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Keystrokes Display

MM 4,027.27 Calculates FV – which equals the

balance in the account if 58 full

deposits were made.*

:P –50.00 Recalls amount of deposits.

+ 3,977.27 Calculates the balance in the account

if 57 full deposits were made and

interest accrued during the 58th

month.†

4000- –22.73 Calculates final, fractional, 58th

deposit required to reach $4,000.

Calculating the Periodic and Annual Interest Rates

1. Press fCLEARG to clear the financial registers.

2. Enter the number of payments or periods, using n or A.

3. Enter at least two of the following values:

z Present value, using $.

z Payment amount, using P.

z Future value, using M.

Note: Remember to

observe the cash flow si

g

n

convention.

4. If a PMT was entered, press g× or gÂ to set the payment mode.

5. Press ¼ to calculate the periodic interest rate.

6. To calculate the annual interest rate, key in the number of periods per year,

then press §.

* In this example, M must be pressed twice, since the preceding key pressed was z. If we

had stored the number of deposits in n (as we did following Example 1), we would have to

press M only once here, since the preceding key pressed would have been w (as it was

following Example 1). Remember that it is not necessary to store the number of payments in n

before calculating the amount of the final, fractional payment. (Refer to the preceding

footnote.)

† You might think that we could calculate the balance in the account after 57 full deposits were

made simply by storing that number in n and then calculating FV, as we did using the second

method following Example 1. However, this balance would not include the interest accrued

during the 58th month.

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Example: What annual interest rate must be obtained to accumulate $10,000 in

8 years on an investment of $6,000 with quarterly compounding?

Keystrokes Display

fCLEARG

8\4§w

32.00

Calculates and stores n.

6000Þ$ –6,000.00 Stores PV (with minus sign for cash

paid out).

10000M 10,000.00 Stores FV.

¼ 1.61 Periodic (quarterly) interest rate.

4§ 6.44 Annual interest rate.

Calculating the Present Value

1. Press fCLEARG to clear the financial registers.

2. Enter the number of payments or periods, using n or A.

3. Enter the periodic interest rate, using ¼ or C.

4. Enter either or both of the following:

z Payment amount, using P.

z Future value, using M.

Note: Remember to

observe the cash flow si

g

n

convention.

5. If a PMT was entered, press g× or gÂ to set the payment mode.

6. Press $ to calculate the present value.

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Example 1: You’re financing a new car purchase with a loan from an institution

that requires 15% interest compounded monthly over the 4-year term of the loan. If

you can make payments of $150 at the end of each month and your down

payment will be $1,500, what is the maximum price you can pay for the car?

(Assume the purchase date is one month prior to the date of the first payment.)

Keystrokes Display

fCLEARG

4gA

48.00

Calculates and stores n.

15gC 1.25 Calculates and stores i.

150ÞP –150.00 Stores PMT (with minus sign for cash

paid out).

gÂ –150.00 Sets payment mode to End.

$ 5,389.72 Maximum amount of loan.

1500+ 6,889.72 Maximum purchase price.

Example 2: A development company would like to purchase a group of

condominiums with an annual net cash flow of $17,500. The expected holding

period is 5 years, and the estimated selling price at that time is $540,000.

Calculate the maximum amount the company can pay for the condominiums in

order to realize at least a 12% annual yield.

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Keystrokes Display

fCLEARG

5n

5.00

Stores n.

12¼ 12.00 Stores i.

17500P 17,500.00 Stores PMT. Unlike in the previous

problem, here PMT is positive

since it represents cash received.

540000M 540,000.00 Stores FV.

gÂ 540,000.00 Sets payment mode to End.

$ –369,494.09 The maximum purchase price to

provide a 12% annual yield. PV is

displayed with a minus sign since

it represents cash paid out.

Calculating the Payment Amount

1. Press fCLEARG to clear the financial registers.

2. Enter the number of payments or periods, using n or A.

3. Enter the periodic interest rate, using ¼ or C.

4. Enter either or both of the following:

z Present value, using $.

z Future value, using M.

Note: Remember to

observe the cash flow si

g

n

convention.

5. Press g× or gÂ to set the payment mode.

6. Press P to calculate the payment amount.

Example 1: Calculate the payment amount on a 29-year, $43,400 mortgage at

141/4% annual interest.

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Keystrokes Display

fCLEARG

29gA

348.00

Calculates and stores n.

14.25gC 1.19 Calculates and stores i.

43400$ 43,400.00 Stores PV.

gÂ 43,400.00 Sets payment mode to End.

P –523.99 Monthly payment (with minus sign

for cash paid out).

Example 2: Looking forward to retirement, you wish to accumulate $60,000

after 15 years by making deposits in an account that pays 93/4% interest

compounded semiannually. You open the account with a deposit of $3,200 and

intend to make semiannual deposits, beginning six months later, from your

profit-sharing bonus paychecks. Calculate how much these deposits should be.

Keystrokes Display

fCLEARG

15\2µw

30.00

Calculates and stores n.

9.75\2z¼ 4.88 Calculates and stores i.

3200Þ$ –3200.00 Stores PV (with minus sign for cash

paid out).

60000M 60,000.00 Stores FV.

gÂ 60,000.00 Sets payment mode to End.

P –717.44 Semiannual payment (with minus sign

for cash paid out).

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Calculating the Future Value

1. Press fCLEARG to clear the financial registers.

2. Enter the number of payments or periods, using n or A.

3. Enter the periodic interest rate, using ¼ or C.

4. Enter either or both of the following:

z Present value, using $.

z Payment amount, using P.

Note: Remember to

observe the cash flow si

g

n

convention.

5. If a PMT was entered, press g× or gÂ to set the payment mode.

6. Press M to calculate the future value.

Example 1: In Example 1 on page 46, we calculated that the payment amount

on a 29-year, $43,400 mortgage at 141/4% annual interest is $523.99. If the

seller requests a balloon payment at the end of 5 years, what would be the

amount of the balloon?

Keystrokes Display

fCLEARG

5gA

60.00

Calculates and stores n.

14.25gC 1.19 Calculates and stores i.

43400$ 43,400.00 Stores PV.

523.99ÞP –523.99 Stores PMT (with minus sign for cash

paid out).

gÂ –523.99 Sets payment mode to End.

M –42,652.37 Amount of balloon payment.

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Example 2: If you deposit $50 a month (at the beginning of each month) into a

new account that pays 61/4% annual interest compounded monthly, how much will

you have in the account after 2 years?

Keystrokes Display

fCLEARG

2gA

24.00

Calculates and stores n.

6.25gC 0.52 Calculates and stores i.

50ÞP –50.00 Stores PMT (with minus sign for cash

paid out).

g× –50.00 Sets payment mode to Begin.

M 1,281.34 Balance after 2 years.

Example 3: Property values in an unattractive area are depreciating at the rate

of 2% per year. Assuming this trend continues, calculate the value in 6 years of

property presently appraised at $32,000.

Keystrokes Display

fCLEARG

6n

6.00

Stores n.

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Keystrokes Display

2Þ¼ –2.00 Stores i (with minus sign for a

“negative interest rate”).

32000Þ $ –32,000.00 Stores PV (with minus sign for cash

paid out).

M 28,346.96 Property value after 6 years.

Odd-Period Calculations

The cash flow diagrams and examples presented so far have dealt with financial

transactions in which interest begins to accrue at the beginning of the first regular

payment period. However, interest often begins to accrue prior to the beginning of

the first regular payment period. The period from the date interest begins accruing

to the date of the first payment, being not equal to the regular payment periods is

sometimes referred to as an “odd first period”. For simplicity, in using the hp 12c

we will always regard the first period as equal to the remaining periods, and we

will refer to the period between the date interest begins accruing and the

beginning of the first payment period as simply the “odd period” or the “odd

days”. (Note that the odd period is always assumed by the calculator to occur

before the first full payment period.) The following two cash flow diagrams

represent transactions including an odd period for payments in advance (Begin)

and for payments in arrears (End).

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You can calculate i, PV, PMT, and FV for transactions involving an odd period

simply by entering a noninteger n. (A noninteger is a number with at least one

nonzero digit to the right of the decimal point.) This places the calculator in

Odd-Period mode.* The integer part of n (the part to the left of the decimal point)

specifies the number of full payment periods, and the fractional part (the part to the

right of the decimal) specifies the length of the odd period as a fraction of a full

period. The odd period, therefore, cannot be greater than one full period.

The fractional part of n can be determined using either the actual number of odd

days or the number of odd days counted on the basis of a 30-day month.† The

Ò function can be used to calculate the number of odd days either way. The

fractional part of n is a fraction of a payment period, so the number of odd days

must be divided by the number of days in a period. If interest is compounded

monthly, for this number you can use either 30, 365/12, or (if the odd period falls

entirely within a single month) the actual number of days in that month. Usually, a

monthly period is taken to be 30 days long.

At your option, the calculations of i, PV, PMT, and FV can be performed with either

simple interest or compound interest accruing during the odd period. If the C status

indicator in the display is not lit, simple interest is used. To specify compound

interest, turn the C indicator on by pressing ?Æ.‡ Pressing ?Æ again

turns the C indicator off, and calculations will then be performed using simple

interest for the odd period.

* Calculations of i, PMT, and FV are performed using the present value at the end of the odd

period. This is equal to the number in the PV register plus the interest accrued during the odd

period. When calculating PV in Odd-Period mode, the calculator returns a value equal to the

present value at the beginning of the odd period and stores it in the PV register.

After calculating i, PV, PMT, or FV in Odd-Period mode, you should not try to calculate n. If

you do, the calculator will switch out of Odd-Period mode and compute n without taking the

odd period into account. The values in the other financial registers will correspond to the new

n, but the original assumptions for the problem will be changed.

† The two methods of counting odd days will yield slightly different answers. If you are

calculating i to determine the annual percentage rate (APR) for an odd-period transaction, the

lower APR will result if the calculation uses the greater number of odd days determined using

the two methods.

‡ ?Æ is not programmable.

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Example 1: A 36-month loan for $4,500 accrues interest at a 15% annual

percentage rate (APR), with the payments made at the end of each month. If

interest begins accruing on this loan on February 15, 2004 (so that the first period

begins on March 1, 2004), calculate the monthly payment, with the odd days

counted on the basis of a 30-day month and compound interest used for the odd

period.

Keystrokes Display

fCLEARG Clears financial registers.

gÕ Sets date format to month-day-year.

gÂ Sets payment mode to End.

?Æ Turns on the

Cindicator in the display,

so that compound interest will be used

for the odd period.

2.152004\ 2.15 Keys in the date interest begins

accruing and separates it from the

next date entered.

3.012004 3.012004 Keys in the date of the beginning of

the first period.

gÒ 15.00 Actual number of odd days.

~ 16.00 Number of odd days counted on the

basis of a 30-day month.

30z 0.53 Divides by the length of a monthly

period to get the fractional part of n.

36+n 36.53 Adds the fractional part of n to the

number of complete payment periods,

then stores the result in n.

15gC 1.25 Calculates and stores i.

4500$ 4,500.00 Stores PV.

P –157.03 Monthly payment.

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Example 2: A 42-month car loan for $3,950 began accruing interest on July 19,

2004, so that the first period began on August 1, 2004. Payments of $120 are

made at the end of each month. Calculate the annual percentage rate (APR), using

the actual number of odd days and simple interest for the odd period.

Keystrokes Display

fCLEARG Clears financial registers.

?Æ Turns off the Cindicator in the display,

so that simple interest will be used for

the odd period.

7.192004\ 7.19 Keys in the date interest begins

accruing and separates it from the

next date entered.

8.012004 8.012004 Keys in the date of the beginning of

the first period.

gÒ 13.00 Actual number of odd days.

30z 0.43 Divides by the length of a monthly

period to get the fractional part of n.

42+n 42.43 Adds the fractional part of n to the

number of complete payment periods,

then stores the result in n.

3950$ 3,950.00 Stores PV.

120ÞP –120.00 Stores PMT (with minus sign for cash

paid out).

¼ 1.16 Periodic (monthly) interest rate.

12§ 13.95 Annual percentage rate (APR).

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Amortization

The hp 12c enables you to calculate the amounts applied toward principal and

toward interest from a single loan payment or from several payments, and also

tells you the remaining balance of the loan after the payments are made.*

To obtain an amortization schedule:

1. Press fCLEARG to clear the financial registers.

2. Enter the periodic interest rate, using ¼ or C.

3. Enter the amount of the loan (the principal), using $.

4. Key in the periodic payment, then press ÞP (the sign of PMT must be

negative, in accordance with the cash flow sign convention).

5. Press g× or (for most direct reduction loans) gÂ to set the payment

mode.

6. Key in the number of payments to be amortized.

7. Press

f! to display the amount from those payments applied toward

interest.

8. Press ~ to display the amount from those payments applied toward the

principal.

9. To display the number of payments just amortized, press dd.

10. To display the remaining balance of the loan, press :$.

11.To display the total number of payments amortized, press :n.

Example: For a house you’re about to buy, you can obtain a 25-year mortgage

for $50,000 at 131/4% annual interest. This requires payments of $573.35 (at the

end of each month). Find the amounts that would be applied to interest and to the

principal from the first year’s payments.

Keystrokes Display

fCLEARG

13.25gC

1.10

Enters i.

50000$ 50,000.00 Enters PV.

* All amounts calculated when f! is pressed are automatically rounded to the number of

decimal places specified by the display format. (The display format is described in Section 5.)

This rounding affects the number inside the calculator as well as how the number appears in

the display. The amounts calculated on your hp 12c may differ from those on the statements

of lending institutions by a few cents, since different rounding techniques are sometimes used.

To calculate answers rounded to a different number of decimal places, press f followed by

the number of decimal places desired before you press f!.

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Keystrokes Display

573.35ÞP –573.35 Enters PMT (with minus sign for cash

paid out).

gÂ –573.35 Sets payment mode to End.

12f! –6,608.89 Portion of first year’s payments (12

months) applied to interest.

~ –271.31 Portion of first year’s payments

applied to principal.

:$ 49,728.69 Balance remaining after 1 year.

:n 12.00 Total number of payments amortized.

The number of payments keyed in just before f! is pressed is taken to be the

payments following any that have already been amortized. Thus, if you now press

12f!, your hp 12c will calculate the amounts applied to interest and to the

principal from the second year’s payments (that is, the second 12 months):

Keystrokes Display

12f! –6,570.72 Portion of second year’s payments

applied to interest.

~ –309.48 Portion of second year’s payments

applied to principal.

dd 12.00 Number of payments just amortized.

:$ 49,419.21 Balance remaining after 2 years.

:n 24.00 Total number of payments amortized.

Pressing :$ or :n displays the number in the PV or n register. When you

did so after each of the last two calculations, you may have noticed that PV and n

had been changed from their original values. The calculator does this so that you

can easily check the remaining balance and the total number of payments

amortized. But because of this, if you want to generate a new amortization

schedule from the beginning, you must reset PV to its original value and reset n to

0.

For example, suppose you now wanted to generate an amortization schedule for

each of the first two months:

Keystrokes Display

50000$ 50,000.00 Resets PV to original value.

0n 0.00 Resets n to zero.

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Keystrokes Display

1f! –552.08 Portion of first payment applied to

interest.

~ –21.27 Portion of first payment applied to

principal.

1f! –551.85 Portion of second payment applied to

interest.

~ –21.50 Portion of second payment applied to

principal.

:n 2.00 Total number of payments amortized.

If you want to generate an amortization schedule but do not already know the

monthly payment:

1. Calculate PMT as described on page 46.

2. Press 0n to reset n to zero.

3. Proceed with the amortization procedure listed on page 54 beginning with

step 6.

Example: Suppose you obtained a 30-year mortgage instead of a 25-year

mortgage for the same principal ($50,000) and at the same interest rate (131/4%)

as in the preceding example. Calculate the monthly payment, then calculate the

amounts applied to interest and to the principal from the first month’s payment.

Since the interest rate is not being changed, do not press fCLEARG; to

calculate PMT, just enter the new value for n, reset PV, then press P.

Keystrokes Display

30gA 360.00 Enters n.

50000$ 50,000.00 Enters PV.

P –562.89 Monthly payment.

0n 0.00 Resets n to zero.

1f! –552.08 Portion of first payment applied to

interest.

~ –10.81 Portion of first payment applied to

principal.

:$ 49,989.19 Remaining balance.

57

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Section 4

Additional Financial

Functions

Discounted Cash Flow Analysis: NPV and IRR

The hp 12c provides functions for the two most widely-used methods of discounted

cash flow analysis: l (net present value) and L (internal rate of return). These

functions enable you to analyze financial problems involving cash flows (money

paid out or received) occurring at regular intervals. As in compound interest

calculations, the interval between cash flows can be any time period; however, the

amounts of these cash flows need not be equal.

To understand how to use l and L, let’s consider the cash flow diagram for

an investment that requires an initial cash outlay (CF0) and generates a cash flow

(CF1) at the end of the first year, and so on up to the final cash flow (CF6) at the

end of the sixth year. In the following diagram, the initial investment is denoted by

CF0, and is depicted as an arrow pointing down from the time line since it is cash

paid out. Cash flows CF1 and CF4 also point down from the time line, because they

represent projected cash flow losses.

NPV is calculated by adding the initial investment (represented as a negative cash

flow) to the present value of the anticipated future cash flows. The interest rate, i,

will be referred to in this discussion of NPV and IRR as the rate of return.* The

value of NPV indicates the result of the investment:

* Other terms are sometimes used to refer to the rate of return. These include: required rate of

return, minimally acceptable rate of return, and cost of capital.

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z If NPV is positive, the financial value of the investor’s assets would be

increased: the investment is financially attractive.

z If NPV is zero, the financial value of the investor’s assets would not change:

the investor is indifferent toward the investment.

z If NPV is negative, the financial value of the investor’s assets would be

decreased: the investment is not financially attractive.

A comparison of the NPV’s of alternative investment possibilities indicates which of

them is most desirable: the greater the NPV, the greater the increase in the

financial value of the investor’s assets.

IRR is the rate of return at which the discounted future cash flows equal the initial

cash outlay: IRR is the discount rate at which NPV is zero. The value of IRR relative

to the present value discount rate also indicates the result of the investment:

z If IRR is greater than the desired rate of return, the investment is financially

attractive.

z If IRR is equal to the desired rate of return, the investor is indifferent toward

the investment.

z If IRR is less than the desired rate of return, the investment is not financially

attractive.

Calculating Net Present Value (NPV)

Calculating NPV for Ungrouped Cash Flows. If there are no equal

consecutive cash flows, use the procedure described (and then summarized) below.

With this procedure, NPV (and IRR) problems involving up to 20 cash flows (in

addition to the initial investment CF0) can be solved. If two or more consecutive

cash flows are equal — for example, if the cash flows in periods three and four

are both $8,500 — you can solve problems involving more than 20 cash flows, or

you can minimize the number of storage registers required for problems involving

less than 20 cash flows, by using the procedure described next (under Calculating

NPV for Grouped Cash Flows, page 61).

The amount of the initial investment (CF0) is entered into the calculator using the

J key. Pressing gJ stores CF0 in storage register R0 and also stores the

number 0 in the n register.

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The amounts of the subsequent cash flows are stored – in the order they occur – in

the remaining storage registers: CF1 thru CF9 in R1 thru R9, and CF10 thru CF19 in R.0

thru R.9, respectively. If there is a CF20, that amount is stored in the FV register.*

Each cash flow (CF1, CF2, etc.) is designated CFj, where j takes on values from 1

up to the number of the final cash flow. The amount of a cash flow is entered using

the K key. Each time gK is pressed, the amount in the display is stored in

the next available storage register, and the number in the n register is increased

by 1. This register therefore counts how many cash flow amounts (in addition to

the initial investment CF0) have been entered.

Note: When entering cash flow amounts — including the initial investment

CF0 — remember to observe the cash flow sign convention by pressing Þ

after keying in a negative cash flow.

In summary, to enter the cash flow amounts:

1. Press fCLEARH to clear the financial and storage registers.

2. Key in the amount of the initial investment, press Þ if that cash flow is

negative, then press gJ. If there is no initial investment, press 0gJ.

3. Key in the amount of the next cash flow, press Þ if the cash flow is

negative, then press gK. If the cash flow amount is zero in the next

period, press 0 gK.

4. Repeat step 3 for each cash flow until all have been entered.

With the amounts of the cash flows stored in the calculator’s registers, you can

calculate NPV as follows:

1. Enter the interest rate, using ¼ or C.

2. Press fl.

The calculated value of NPV appears in the display and also is automatically

stored in the PV register.

* If you have stored a program in the calculator, the number of registers available for storing

cash flow amounts may be less than 21. (Storage registers are automatically allocated to

program lines beginning with R.9 and proceeding in reverse order to R7, as described on

pages 93 thru 95.) The maximum number of cash flow amounts (in addition to CF0) that can

be stored is the number that appears at the right of the display when gN is pressed. If the

maximum number of cash flow amounts is stored, the final cash flow amount is always stored

in the FV register. For example, if N displays P-08 r-20, the last cash flow amount that can

be stored – CF20 – will be stored in FV. Similarly, if N displays P-22 r-18, the last cash

flow amount that can be stored – CF18 – will be stored in FV.

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Example: An investor has an opportunity to buy a duplex for $80,000 and

would like a return of at least 13%. He expects to keep the duplex 5 years and

then sell it for $130,000; and he anticipates the cash flows shown in the diagram

below. Calculate NPV to determine whether the investment would result in a return

or a loss.

Note that although a cash flow amount ($4,500) occurs twice, these cash flows

are not consecutive. Therefore, these cash flows must be entered using the method

described above.

Keystrokes Display

fCLEARH 0.00 Clears financial and storage registers.

80000ÞgJ –80,000.00 Stores CF0 (with minus sign for a

negative cash flow).

500ÞgK –500.00 Stores CF1 (with minus sign for a

negative cash flow).

4500gK 4,500.00 Stores CF2.

5500gK 5,500.00 Stores CF3.

4500gK 4,500.00 Stores CF4.

130000gK 130,000.00 Stores CF5.

:n 5.00 Checks number of cash flow amounts

entered (in addition to CF0 ).

13¼ 13.00 Stores i.

fl 212.18 NPV.

Since NPV is positive, the investment would increase the financial value of the

investor’s assets.

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Calculating

NPV

for Grouped Cash Flows. A maximum of 20 cash flow

amounts (in addition to the initial investment CF0) can be stored in the hp 12c.*

However, problems involving more than 20 cash flows can be handled if among

the cash flows there are equal consecutive cash flows. For such problems, you

merely enter along with the amounts of the cash flows the number of times — up to

99 — each amount occurs consecutively. This number is designated Nj,

corresponding to cash flow amount CFj, and is entered using the a key. Each Nj

is stored in a special register inside the calculator.

This method can, of course, be used for problems involving fewer than 20 cash

flows — and it will require fewer storage registers than the method described

above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive cash

flows can be entered using that method — provided there are enough storage

registers available to accommodate the total number of individual cash flows. The

facility of grouping equal consecutive cash flows is provided to minimize the

number of storage registers required.

Note: When entering cash flow amounts — including the initial investment

CF0 — remember to observe the cash flow sign convention by pressing Þ

after keying in the amount for a negative cash flow.

In summary, to enter the amounts of the cash flows and the number of times they

occur consecutively:

1. Press fCLEARH to clear the financial and storage registers.

2. Key in the amount of the initial investment, press Þ if that cash flow is

negative, then press gJ. If there is no initial investment, press 0gJ.

3. If the initial investment consists of more than one cash flow of the amount

entered in step 2, key in the number of those cash flows, then press ga. If

ga is not pressed, the calculator assumes that N0 is 1.

4. Key in the amount of the next cash flow, press Þ if that cash flow is

negative, then press gK. If the cash flow amount is zero in the next

period, press 0gK.

5. If the amount entered in step 4 occurs more than once consecutively, key in

the number of times that cash flow amount occurs consecutively, then press

ga. If ga is not pressed, the calculator assumes that Nj is 1 for the CFj

just entered.

6. Repeat steps 4 and 5 for each CFj and Nj until all cash flows have been

entered.

With the amounts of the cash flows and the number of times they occur

consecutively stored in the calculator, NPV can be calculated by entering the

interest rate and pressing fl, just as described earlier.

* If you have stored a program in the calculator, the number of registers available for storing

cash flow amounts may be less than 21.

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Example: An investor has an opportunity to purchase a piece of property for

$79,000; and he would like a 131/2% return. He expects to be able to sell it after

10 years for $100,000 and anticipates the yearly cash flows shown in the table

below:

Year Cash Flow Year Cash Flow

1

2

3

4

5

$14,000

$11,000

$10,000

$10,000

$10,000

6

7

8

9

10

$9,100

$9,000

$9,000

$4,500

$100,000

Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively,

we can minimize the number of storage registers required by using the method just

described.

Keystrokes Display

fCLEARH 0.00 Clears financial and storage

registers.

79000ÞgJ –79,000.00 Initial investment (with minus si

g

n for

a negative cash flow).

14000gK 14,000.00 First cash flow amount.

11000gK 11,000.00 Next cash flow amount.

10000gK 10,000.00 Next cash flow amount.

3ga 3.00 Number of times this cash flow

amount occurs consecutively.

9100gK 9,100.00 Next cash flow amount.

9000gK 9,000.00 Next cash flow amount.

2ga 2.00 Number of times this cash flow

amount occurs consecutively.

4500gK 4,500.00 Next cash flow amount.

100000gK 100,000.00 Final cash flow amount.

:n 7.00 Seven different cash flow amounts

have been entered.

13.5¼ 13.50 Stores i.

fl 907.77 NPV.

Since NPV is positive, the investment would increase the financial value of the

investor’s assets by $907.77.

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Calculating Internal Rate of Return (IRR)

1. Enter the cash flows using either of the methods described above under

Calculating Net Present Value.

2. Press fL.

The calculated value of IRR appears in the display and also is automatically stored

in the i register.

Note: Remember that the L function may take a significant amount of

time to produce an answer, during which the calculator displays running.

Example: The NPV calculated in the preceding example was positive, indicating

that the actual rate of return (that is, the IRR) was greater than the 131/2 used in the

calculation. Find the IRR.

Assuming the cash flows are still stored in the calculator, we need only press

fL:

Keystrokes Display

fL 13.72 IRR is 13.72%.

Note that the value calculated by L is the periodic rate of return. If the cash flow

periods are other than years (for example, months or quarters), you can calculate

the nominal annual rate of return by multiplying the periodic IRR by the number of

periods per year.

As noted above, the calculator may take several seconds or even minutes to

produce an answer for IRR. This is because the mathematical calculations for

finding IRR are extremely complex, involving a series of iterations — that is, a

series of successive calculations. In each iteration, the calculator uses an estimate

of IRR as the interest rate in a computation of NPV. The iterations are repeated

until the computed NPV reaches about zero.*

If you do not want to wait for the computation of IRR to be completed, press any

key. This halts the computation of IRR and displays the estimated value of IRR being

used in the current iteration.† You can then check how good this estimate is by

calculating NPV using this estimate: if the estimate is close to IRR, the NPV

calculated with it should be close to zero.* The values of IRR is put into the i

register at the end of each iteration. Therefore, to check how good an estimate of

IRR is after that estimate is in the display, just press fl.

* In practice, because the complex mathematical calculations inside the calculator are done

with numbers rounded to 10 digits, NPV may never reach exactly zero. Nevertheless, the

interest rate that results in a very small NPV is very close to the actual IRR.

† Provided the first iteration has been completed.

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The complex mathematical characteristics of the IRR computation have an

additional ramification: Depending on the magnitudes and signs of the cash flows,

the computation of IRR may have a single answer, multiple answers, a negative

answer or no answer.*

For additional information regarding L, refer to Appendix B. For an alternative

method of calculating IRR, refer to Section 13.

Reviewing Cash Flow Entries

z To display a single cash flow amount, press :, then key in the number of

the register containing the cash flow amount to be displayed. Alternatively,

store the number of that cash flow amount (that is, the value of j for the CFj

desired) in the n register, then press :gK.

z To review all the cash flow amounts, press :g K repeatedly. This

displays the cash flow amounts in reverse order — that is, beginning with the

final cash flow and proceeding to CF0.

z To display the number of times a cash flow amount occurs consecutively —

that is, to display the Nj for a CFj — store the number of that cash flow

amount (that is, the value of j) in the n register, then press :ga.

z To review all the cash flow amounts together with the number of times each

cash flow amount occurs consecutively (that is, to review each CFj and Nj

pair), press :ga:gK repeatedly. This displays Nj followed by

CFj beginning with the final cash flow amount and proceeding to N0 and

CF0.

Note: Neither L nor l change the number in the n register. However,

each time :gK is pressed, the number in the n register is decreased

by 1. If this is done, or if you manually change the number in the n register

in order to display a single Nj and/or CFj, be sure to reset the number in the

n register to the total number of cash flow amounts originally entered (not

including the amount of the initial investment CF0). If this is not done, NPV

and IRR calculations will give incorrect results; also, a review of cash flow

entries would begin with Nn and CFn, where n is the number currently in the

n register.

For example, to display the fifth cash flow amount and the number of times that

amount occurs consecutively:

Keystrokes Display

:5 9,000.00 CF5

5n 5.00 Stores the value of j in the n register.

* In the case of multiple answers for IRR, the decision criteria listed on page 57 should be

modified accordingly.

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Keystrokes Display

:ga 2.00 N5

7n 7.00 Resets the number in the n re

g

ister to

its original value.

To display all the cash flow amounts and the number of times they occur

consecutively:

Keystrokes Display

:ga 1.00 N7

:gK 100,000.00 CF7

:ga 1.00 N6

:gK 4,500.00 CF6

:ga 2.00 N5

:gK 9,000.00 CF5

.

.

.

.

.

.

.

.

.

:ga 1.00 N1

:gK 14,000.00 CF1

:ga 1.00 N0

:gK –79,000.00 CF0

7n 7.00 Resets the number in the n register

to its original value.

Changing Cash Flow Entries

z To change a cash flow amount:

1. Key the amount into the display.

2. Press ?.

3. Key in the number of the register containing the cash flow amount to be

changed.

z To change the number of times a cash flow amount occurs consecutively —

that is, to change the Nj for a CFj:

1. Store the number of that cash flow amount (that is, j) in the n register.

2. Key the number of times the cash flow amount occurs consecutively into

the display.

3. Press ga.

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Note: If you change the number in the n register in order to change an Nj,

be sure to reset the number in the n register to the total number of cash flow

amounts originally entered (not including the amount of the initial investment

CF0). If this is not done, NPV and IRR calculations will give incorrect results.

Example 1: With the cash flows now stored in the calculator, change CF2 from

$11,000 to $9,000, then calculate the new NPV for a 131/2% return.

Keystrokes Display

9000?2 9,000.00 Stores the new CF2 in R2.

13.5¼ 13.50 Stores i.*

fl –644.75 The new NPV.

Since this NPV is negative, the investment would decrease the financial value of

the investor’s assets.

Example 2: Change N5 from 2 to 4, then calculate the new NPV.

Keystrokes Display

5n 5.00 Stores j in the n register.

4ga 4.00 Stores the new N5.

7n 7.00 Resets the number in the n register

to its original value.

fl –1,857.21 The new NPV.

Bond Calculations

The hp 12c enables you to solve for bond price (and the interest accrued since the

last interest date) and the yield to maturity.† The E and S calculations are

done assuming a semiannual coupon payment and using an actual/actual basis

(such as for U.S. Treasury bonds and U.S. Treasury notes). In accordance with

market convention, prices are based on a redemption (par) value of 100.

* This step is necessary in this example because we have calculated IRR since the first time we

calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before calculating

NPV with the result for IRR – 13.72.

† All bond calculations are performed in accordance with. the Securities Industry Association’s

recommendations as contained in Spence, Graudenz, and Lynch, Standard Securities

Calculation Methods, Securities Industry Association, New York, 1973.

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To calculate bond price and yield for a 30/360 bond (that is, using the basis of a

30day month and a 360-day year — such as for municipal bonds, corporate

bonds, and state and local government bonds), and to calculate bond price for

bonds with an annual coupon payment, refer to Section 16: Bonds.

Bond Price

1. Enter the desired yield to maturity (as a percentage), using ¼.

2. Enter the annual coupon rate (as a percentage), using P.

3. Key in the settlement (purchase) date (as described on page 29), then press

\.

4. Key in the maturity (redemption) date.

5. Press fE.

The price is shown in the display and also is stored in the PV register. The interest

accrued since the last interest date is held inside the calculator: to display the

interest, press ~; to add the interest to the price, press +.

Example: What price should you pay on April 28, 2004 for a 63/4% U.S.

Treasury bond that matures on June 4, 2018, if you want a yield of 81/4%.

Assume that you normally express dates in the month-day-year format.

Keystrokes Display

8.25¼ 8.25 Enters yield to maturity.

6.75P 6.75 Enters coupon rate.

gÕ 6.75 Sets date format to month-day-year.

4.282004\ 4.28 Enters settlement (purchase) date.

6.042018 6.042018 Enters maturity (redemption) date.

fE 87.62 Bond price (as a percent of par).

+ 90.31 Total price, including accrued

interest.

Bond Yield

1. Enter the quoted price (as a percent of par), using $.

2. Enter the annual coupon rate (as a percentage), using P.

3. Key in the settlement (purchase) date, then press \.

4. Key in the maturity (redemption) date.

5. Press fS.

The yield to maturity is shown in the display and also is stored in the i register.

Note: Remember that the S function may take a significant amount of

time to produce an answer, during which the calculator displays running.

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Example: The market is quoting 883/8% for the bond described in the preceding

example. What yield will that provide?

Keystrokes Display

3\8z 0.38 Calculates 3/8.

88+$ 88.38 Enters quoted price.

6.75P 6.75 Enters coupon rate.

4.282004\ 4.28 Enters settlement (purchase) date.

6.042018 6.042018 Enters maturity (redemption) date.

fS 8.15 Bond yield.

Depreciation Calculations

The hp 12c enables you to calculate depreciation and the remaining depreciable

value (book value minus salvage value) using the straight-line,

sum-of-the-years-digits, and declining-balance methods. To do so with any of these

methods:

1. Enter the original cost of the asset, using $.

2. Enter the salvage value of the asset, using M. If the salvage value is zero,

press 0M.

3. Enter the expected useful life of the asset (in years), using n.

4. If the declining-balance method is being used, enter the declining-balance

factor (as a percentage), using ¼. For example, 11/4 times the straight-line

rate — 125 percent declining-balance — would be entered as 125¼.

5. Key in the number of the year for which depreciation is to be calculated.

6. Press:

z fV for depreciation using the straight-line method.

z fÝ for depreciation using the sum-of-the-years digits method.

z f# for depreciation using the declining-balance method.

V, Ý, and #

each place the amount of depreciation in the display. To

display the remaining depreciable value (the book value less the salvage value)

after the depreciation has been calculated, press ~.

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Example: A metalworking machine, purchased for $10,000, is depreciated over

5 years. Its salvage value is estimated at $500. Find the depreciation and

remaining depreciable value for the first 3 years of the machine’s life using the

declining-balance method at double the straight-line rate (200 percent

declining-balance).

Keystrokes Display

10000$ 10,000.00 Enters original cost.

500M 500.00 Enters salvage value.

5n 5.00 Enters expected useful life.

200¼ 200.00 Enters declining-balance factor.

1f# 4,000.00 Depreciation in first year.

~ 5,500.00 Remaining depreciable value after

first year.

2f# 2,400.00 Depreciation in second year.

~ 3,100.00 Remaining depreciable value after

second year.

3f# 1,440.00 Depreciation in third year.

~ 1,660.00 Remaining depreciable value after

third year.

To calculate depreciation and the remaining depreciable value when the

acquisition date of the asset does not coincide with the beginning of the fiscal

accounting year, refer to the procedures in Section 13. That section also includes a

procedure for depreciation calculations when changing from the declining-balance

method to the straight-line method, and a procedure for calculating excess

depreciation.

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Section 5

Additional Operating

Features

Continuous Memory

The calculator’s Continuous Memory contains the data storage registers, the

financial registers, the stack and LAST X registers, program memory, and status

information such as display format, date format, and payment mode. All

information in Continuous Memory is preserved even while the calculator is turned

off. Furthermore, information in Continuous Memory is preserved for a short time

when the batteries are removed, so that you can change the batteries without

losing your data and programs.

Continuous Memory may be reset if the calculator is dropped or otherwise

traumatized, or if power is interrupted. You can also manually reset Continuous

Memory as follows:

1. Turn the calculator off.

2. Hold down the - key, and press ;.

When Continuous Memory is reset:

z All registers are cleared.

z Program memory consists of eight program lines, each containing the

instruction g(00.

z Display format is set to the standard format with two decimal places.

z Date format is set to month-day-year.

z Payment mode is set to End.

Whenever Continuous Memory has been reset, the display will show Pr Error.

Pressing any key will clear this message from the display.

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The Display

Status Indicators

Six indicators that appear along the bottom of the display signify the status of the

calculator for certain operations. These status indicators are described elsewhere

in this handbook where the relevant operation is discussed.

Number Display Formats

When the calculator is first turned on after coming from the factory or after

Continuous Memory has been reset, answers are displayed with two decimal

places.

Keystrokes Display

19.8745632\ 19.87

5- 14.87

Although you see only two decimal places, all calculations in your hp 12c are

performed with full 10-digit numbers.

When only two decimal places are displayed, numbers are rounded to two

decimal places: if the third digit is 5 through 9, the second digit is increased by

one; if the third digit is 0 through 4, the second digit is not affected. Rounding

occurs regardless of how many decimal places are displayed.

Several options are provided for controlling how numbers appear in the display.

But regardless of which display format or how many displayed decimal places you

specify, the number inside the calculator — which appears altered in the

display — is not altered unless you use the B, !, V, Ý, or # functions.

Standard Display Format. The number 14.87 now in your calculator is

currently being displayed in the standard display format with two decimal places

shown. To display a different number of decimal places, press f followed by a

digit key (0 through 9) specifying the number of decimal places. In the following

examples, notice how the displayed form of the number inside the calculator —

14.87456320 — is rounded to the specified number of digits.

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Keystrokes Display

f4 14.8746

f1 14.9

f0 15.

f9 14.87456320 Although nine decimal places were

specified after f, only eight are

displayed since the display can

show a total of only 10 digits.

The standard display format, plus the specified number of decimal places, remain

in effect until you change them; they are not reset each time the calculator is turned

on. However, if Continuous Memory is reset, when the calculator is next turned on

numbers will be displayed in the standard display format with two decimal places

shown.

If a calculated answer is either too small or too large to be displayed in the

standard display format, the display format automatically switches to scientific

notation (described below). The display returns to the standard display format for

all numbers that can be displayed in that format.

Scientific Notation Display Format

In scientific notation, a number is displayed with its mantissa at the left and a

two-digit exponent at the right. The mantissa is simply the first seven digits in the

number, and has a single, nonzero digit to the left of the decimal point. The

exponent is simply how many decimal places you would move the decimal point in

the mantissa before writing down the number in standard format. If the exponent is

negative (that is, there is a minus sign between it and the mantissa), the decimal

point should be moved to the left; this occurs for any number less than 1. If the

exponent is positive (that is, there is a blank space between it and the mantissa),

the decimal point should be moved to the right; this occurs for any number greater

than or equal to 1.

To set the display format to scientific notation, press f.. For example (assuming

the display still shows 14.87456320 from the preceding example):

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Keystrokes Display

f. 1.487456 01

The exponent in this example indicates that the decimal point should be moved

one decimal place to the right, giving the number 14.87456, which is the first

seven digits of the number previously in the display.

To set the display back to standard display format, press f followed by the

desired number of decimal places. Scientific notation display format remains in

effect until you change to the standard display format; it is not reset each time the

calculator is turned on. However, if Continuous Memory is reset, when the

calculator is next turned on the standard display format, with two decimal places,

will be used.

Mantissa Display Format. Because both the standard display format and

scientific notation display format often show only a few digits of a number, you

may occasionally want to see all 10 digits — the full mantissa — of the number

inside the calculator. To do so, press fCLEARX and hold down the X key.

The display will show all 10 digits of the number as long as you hold down the

X key; after you release the key, the number will again be displayed in the

current display format. For instance, if the display still contains the result from the

preceding example:

Keystrokes Display

fCLEARX 1487456320 All 10 digits of the number inside

the calculator.

1.487456 01 Display returns to its former contents

when the X key is released.

f2 14.87 Returns display to standard format.

Special Displays

Running. Certain functions and many programs may take several seconds or

more to produce an answer. During these calculations, the word running flashes

in the display to let you know that the calculator is running.

Overflow and Underflow. If a calculation results in a number whose

magnitude is greater than 9.999999999 ×1099, the calculation is halted and the

calculator displays 9.999999 99 (if the number is positive) or –9.999999 99

(if the number is negative).

If a calculation results in a number whose magnitude is less than 10–99, the

calculation is not halted, but the value 0 is used for that number in subsequent

calculations.

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Errors. If you attempt an improper operation — such as division by zero — the

calculator will display the word Error followed by a digit (0 through 9). To clear

the Error display, press any key. This does not execute that key’s function, but

does restore the calculator to its condition before the improper operation was

attempted. Refer to Appendix C for a list of error conditions.

Pr Error. If power to the calculator is interrupted, the calculator will display Pr

Error when next turned on. This indicates that Continuous Memory — which

contains all data, program, and status information — has been reset.

The key

Suppose you need to subtract $25.83 from $144.25, and you (mistakenly) key in

25.83, press \, then key in 144.25. But then you realize that when written

down on paper, the desired calculation reads 144.25 – 25.83, so that you have

unfortunately keyed in the second number first. To correct this mistake, merely

exchange the first and second numbers by pressing ~, the exchange key.

Keystrokes Display

25.83\144.25 144.25 Oops! You mistakenly keyed in the

second number first.

~ 25.83 Exchanges the first and second

numbers. The first number keyed in is

now in the display.

- 118.42 The answer is obtained by pressing

the operation key.

The ~ key is also useful for checking the first number entered to make sure you

keyed it in correctly. Before pressing the operation key, however, you should press

~ again to return the second number entered to the display. Regardless of how

many times you press ~, the calculator considers the number in the display to

be the second number entered.

The Key

Occasionally you may want to recall to the display the number that was there

before an operation was performed. (This is useful for doing arithmetic calculations

with constants and for recovering from errors in keying in numbers.) To do so,

press gF (last x).

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Arithmetic Calculations With Constants

Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,

75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.

Keystrokes Display

15\ 15.00 Keys first quantity into calculator.

4.38 4.38 Keys unit cost into display.

§ 65.70 Cost of a package of 15.

75 75. Keys second quantity into display.

gF 4.38 Recalls unit cost — which was last

number in display before § was

pressed — into display.

§ 328.50 Cost of a package of 75.

250 250. Keys third quantity into display.

gF 4.38 Recalls unit cost into display again.

§ 1,095.00 Cost of a package of 250.

Another method for doing arithmetic calculations with constants is described on

page 177.

Recovering From Errors in Digit Entry

Example: Suppose you want to divide the total annual production for one of your

firm’s products (429,000) by the number of retail outlets (987) in order to

calculate the average number distributed by each outlet. Unfortunately, you

mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to

correct:

Keystrokes Display

429000\ 429,000.00

9987 9,987. You haven’t noticed your mistake

yet.

z 42.96 About 43 products per outlet — but

that seems too low!

gF 9,987.00 Recalls to the display the number

that was there before you press z.

You see that you keyed it in wrong.

429000\ 429,000.00 Begins the problem over.

987z 434.65 The correct answer.

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Section 6

Statistics Functions

Accumulating Statistics

The hp 12c can perform one- or two-variable statistical calculations. The data is

entered into the calculator using the _ key, which automatically calculates and

stores statistics of the data into storage registers R1, through R6. (These registers are

therefore referred to as the “statistics registers.”)

Before beginning to accumulate statistics for a new set of data, you should clear

the statistics registers by pressing fclear².*

In one-variable statistical calculations, to enter each data point — referred to as an

“x-value” — key the x-value into the display, then press _.

In two-variable statistical calculations, to enter each data pair — referred to as the

“x and y-values”:

1. Key the y-value into the display.

2. Press \.

3. Key the x-value into the display.

4. Press _.

Each time you press _, the calculator does the following:

z The number in R1 is increased by 1, and the result is copied into the display.

z The x-value is added to the number in R2.

z The square of the x-value is added to the number in R3.

z The y-value is added to the number in R4.

z The square of the y-value is added to the number in R5.

z The product of the x and y-values is added to the number in R6.

* This also clears the stack registers and the display.

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The table below shows where the accumulated statistics are stored.

Register Statistic

R1 (and display) n: number of data pairs accumulated.

R2 Σx: summation of x-values.

R3 Σx2: summation of squares of x-values.

R4 Σy: summation of y-values.

R5 Σy2 summation of squares of y-values.

R6 Σxy: summation of products of x-values and y-values.

Correcting Accumulated Statistics

If you discover you have entered data incorrectly, the accumulated statistics can

easily be corrected:

z If the incorrect data point or data pair has just been entered and _ has

been pressed, press gFg^.

z If the incorrect data point or data pair is not the most recent one entered, key

in the incorrect data point or data pair again as if it were new, but press

g^ instead of _.

These operations cancel the effect of the incorrect data point or data pair. You can

then enter the data correctly, using _, just as if it were new.

Mean

Pressing gÖ calculates the means (arithmetic averages) of the x-values ( x) and

of the y-values ( y). The mean of the x-values appears in the display after Ö is

pressed; to display the mean of the y-values, press ~.

Example: A survey of seven salespersons in your company reveals that they work

the following hours a week and sell the following dollar volumes each month. How

many hours does the average salesperson work each week? How much does the

average salesperson sell each month?

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Salesperson Hours/Week Hours/Week

1 32 $17,000

2 40 $25,000

3 45 $26,000

4 40 $20,000

5 38 $21,000

6 50 $28,000

7 35 $15,000

To find the average workweek and sales of this sample:

Keystrokes Display

fCLEAR² 0.00 Clears statistics registers.

32\

17000_

32.00

1.00

First entry.

40\

25000_

40.00

2.00

Second entry.

45\

26000_

45.00

3.00

Third entry.

40\

20000_

40.00

4.00

Fourth entry.

38\

21000_

38.00

5.00

Fifth entry.

50\

28000_

50.00

6.00

Sixth entry.

35\

15000_

35.00

7.00

Total number of entries in the

sample.

gÖ 21,714.29 Mean dollar sales per month ( x).

~ 40.00 Mean workweek in hours ( y).

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Standard Deviation

Pressing gv calculates the standard deviation of the x-values (sx) and of the

y-values (sy). (The standard deviation of a set of data is a measure of the dispersion

around the mean.) The standard deviation of the x-values appears in the display

after v is pressed; to display the standard deviation of the y-values, press ~.

Example: To calculate the standard deviations of the x-values and of the y-values

from the preceding example:

Keystrokes Display

gv 4,820.59 Standard deviation of sales.

~ 6.03 Standard deviation of hours worked.

The formulas used in the hp 12c for calculating sx, and sy give best estimates of the

population standard deviation based on a sample of the population. Thus, current

statistical convention calls them sample standard deviations. So we have assumed

that the seven salespersons are a sample of the population of all salespersons, and

our formulas derive best estimates of the population from the sample.

What if the seven salespersons constituted the whole population of salespersons.

Then we wouldn’t need to estimate the population standard deviation. We can

find the true population standard deviation (σ) when the data set equals the total

population, using the following keystrokes.*

Keystrokes Display

gÖ 21,714.29 Mean (dollars)

_ 8.00 Number of entries + 1.

gv 4,463.00 σx

~ 5.58 σy

To continue summing data pairs, press gÖg^ before entering more data.

* It turns out that if you sum the mean of the population into the set itself and find the new s,

computed using the formulas on page 192, that s will be the population standard deviation,

σ, of the original set.

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Linear Estimation

With two-variable statistical data accumulated in the statistics registers, you can

estimate a new y-value ( y

ˆ) given a new x-value, and estimate a new x-value ( x

ˆ)

given a new y-value.

To calculate y

ˆ:

1. Key in a new x-value.

2. Press gR.

To calculate x

ˆ:

1. Key in a new y-value.

2. Press gQ.

Example: Using the accumulated statistics from the preceding problem, estimate

the amount of sales delivered by a new salesperson working 48 hours per week.

Keystrokes Display

48gQ 28,818.93 Estimated sales for a 48 hour

workweek.

The reliability of a linear estimate depends upon how closely the data pairs would,

if plotted on a graph, lie in a straight line. The usual measure of this reliability is

the correlation coefficient, r. This quantity is automatically calculated whenever y

ˆ

or x

ˆ is calculated; to display it, press ~. A correlation coefficient close to 1

or –1 indicates that the data pairs lie very close to a straight line. On the other

hand, a correlation coefficient close to 0 indicates that the data pairs do not lie

closely to a straight line; and a linear estimate using this data would not be very

reliable.

Example: Check the reliability of the linear estimate in the preceding example by

displaying the correlation coefficient.

Keystrokes Display

~ 0.90 The correlation coefficient is close to

1, so the sales calculated in the

preceding example is a good

estimate.

To graph the regression line, calculate the coefficients of the linear equation

y = A + Bx.

1. Press 0gR to compute the y-intercept (A).

2. Press 1gR~d~- to compute the slope of the line (B).

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Example: Compute the slope and intercept of the regression line in the preceding

example.

Keystrokes Display

0gR 15.55 y-intercept (A); projected value for x

= 0.

1 gR~d~- 0.001 Slope of the line (B); indicates the

change in the projected values

caused by an incremental chan

g

e in

the x value.

The equation that describes the regression line is:

y = 15.55 + 0.001x

Weighted Mean

You can compute the weighted mean of a set of numbers if you know the

corresponding weights of the items in question.

1. Press fCLEAR².

2. Key in the value of the item and press \, then key in its weight and press

_. Key in the second item’s value, press \, key in the second weight,

and press _. Continue until you have entered all the values of the items and

their corresponding weights. The rule for entering the data is “item \

weight _.”

3. Press g to calculate the weighted mean of the items.

Example: Suppose that you stop during a vacation drive to purchase gasoline at

four stations as follows: 15 gallons at $1.16 per gallon, 7 gallons at $1.24 per

gallon, 10 gallons at $1.20 per gallon, and 17 gallons at $1.18 per gallon. You

want to find the average cost per gallon of gasoline purchased. If you purchased

the same quantity at each station, you could determine the simple arithmetic

average or mean using the Ö key. But since you know the value of the item

(gasoline) and its corresponding weight (number of gallons purchased), use the

key to find the weighted mean:

Keystrokes Display

fCLEAR² 0.00 Clears statistics registers.

1.16\15_ 1.00 First item and weight.

1.24\7_ 2.00 Second item and weight.

1.20\10_ 3.00 Third item and weight.

1.18\17_ 4.00 Fourth item and weight.

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Keystrokes Display

g 1.19 Weighted mean cost per gallon.

A procedure for calculating the standard deviation and standard error (as well as

the mean) of weighted or grouped data is included in the hp 12c Solutions

Handbook.

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Section 7

Mathematics and

Number-Alteration Functions

The hp 12c provides several keys for mathematical functions and for altering,

numbers. These functions are useful for specialized financial calculations as well as

for general mathematics calculations.

One-Number Functions

Most of the mathematics functions require that only one number be in the

calculator (that is, the number in the display) before the function key is pressed.

Pressing the function key then replaces the number in the display by the result.

Reciprocal. Pressing y calculates the reciprocal of the number in the display —

that is, it divides 1 by the number in the display.

Square Root. Pressing gr calculates the square root of the number in the

display.

Logarithm. Pressing g° calculates the natural logarithm (that is, the

logarithm to the base e) of the number in the display. To calculate the common

logarithm (that is, the logarithm to the base 10) of the number in the display,

calculate the natural logarithm, then press 10g°z.

Exponential. Pressing g> calculates the exponential of the number in the

display — that is, it raises the base e to the number in the display.

Factorial. Pressing ge calculates the factorial of the number in the display —

that is, it calculates the product of the integers from 1 to n, where n is the number

in the display.

Round. The display format specifies to how many decimal places a number

inside the calculator is rounded when it appears in the display; but the display

format alone does not affect the number itself inside the calculator. Pressing

fB, however, changes the number inside the calculator to match its displayed

version. Thus, to round a number in the display to a given number of decimal

places, temporarily set the display format (as described on page 71) to show the

desired number of decimal places, then press fB.

Integer. Pressing gÑ replaces the number in the display by its integer

portion — that is, it replaces each digit to the right of the decimal point by 0. The

number is changed inside the calculator as well as in the display. The original

number can be recalled to the display by pressing gF.

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Fractional. Pressing gT replaces the number in the display by its fractional

portion — that is, it replaces all digits to the left of the decimal point by 0. Like

Ñ, T changes the number inside the calculator as well as its displayed

version. The original number can be recalled to the display by pressing gF.

All of the above functions are used basically in the same way. For example, to find

the reciprocal of 0.258:

Keystrokes Display

.258 0.258 Keys the number into the display.

y 3.88 The reciprocal of 0.258, the ori

g

inal

number.

Any of the above functions can be done with a number in the display resulting

from a previous calculation, as well as with a number you have just keyed in.

Keystrokes Display

fCLEARX 3875968992 Displays all 10 digits of the number

inside the calculator.

3.88 Display returns to normal format

when X key is released.

fB 3.88 The number now in the display

appears the same as before, but …

fX 3880000000 Displaying all 10 digits of the

number inside the calculator shows

B has changed the number to

match its displayed version.

3.88 Display returns to normal format.

gÑ 3.00 The integer portion of the number

previously displayed.

gF 3.88 Recalls the original number to the

display.

gT 0.88 The fractional portion of the number

previously displayed.

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The Power Function

Pressing q calculates a power of a number — that is, yx. Like the arithmetic

function +, q requires two numbers:

1. Key in the base number (which is designated by the y on the key).

2. Press \ to separate the second number (the exponent) from the first (the

base).

3. Key in the exponent (which is designated by the x on the key).

4. Press q to calculate the power.

To Calculate Keystrokes Display

21.4 2\1.4q 2.64

2–1.4 2\1.4Þq 0.38

(–2)3 2Þ\3q –8.00

32or 21/3 2\3yq 1.26

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Part II

Programming

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Section 8

Programming Basics

Why Use Programs?

A program is simply a sequence of keystrokes that is stored in the calculator.

Whenever you have to calculate with the same sequence of keystrokes several

times, you can save a great deal of time by incorporating these keystrokes in a

program. Instead of pressing all the keys each time, you press just one key to start

the program: the calculator does the rest automatically!

Creating a Program

Creating a program consists simply of writing the program, then storing it:

1. Write down the sequence of keystrokes that you would use to calculate the

quantity or quantities desired.

2. Press fs to set the calculator to Program mode. When the calculator is

in Program mode, functions are not executed when they are keyed in, but

instead are stored inside the calculator. The PRGM status indicator in the

display is lit when the calculator is in Program mode.

3. Press fCLEARÎ to erase any previous programs that may be stored

inside the calculator. If you want to create a new program without erasing a

program already stored, skip this step and proceed as described in Section

11, Multiple Programs.

4. Key in the sequence of keystrokes that you wrote down in step 1. Skip the

beginning keystrokes that enter data, which would differ each time the

program is used.

Example: Your office supplies dealer is selling selected stock at 25% off. Create

a program that calculates the net cost of an item after the discount is subtracted

and the $5 handling charge is added.

First, we’ll manually calculate the net cost of an item listing for $200.

Keystrokes Display

200 200. Keys in cost of item.

\ 200.00 Separates cost of item from

percentage to be keyed in next.

25b 50.00 Amount of discount.

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Keystrokes Display

- 150.00 Price less discount.

5 5. Handling charge.

+ 155.00 Net cost (price less discount plus

handling charge).

Next, set the calculator to Program mode and erase any program(s) already

stored:

Keystrokes Display

fs 00- Sets calculator to Program mode.

fCLEARÎ 00- Clears program(s).

Finally, press the keys that we used above to solve the problem manually. Do not

key in 200; this number will vary each time the program is used. Don’t be

concerned right now about what appears in the display as you press the keys;

we’ll discuss that later in this section.

Keystrokes Display

\ 01- 36

2 02- 2

5 03- 5

b 04- 25

- 05- 30

5 06- 5

+ 07- 40

Running a Program

To run (sometimes called “execute”) a program:

1. Press fs to set the calculator back to Run mode. If the calculator is

already in Run mode (that is, the PRGM status indicator in the display is not

lit), skip this step.

2. Key any required data into the calculator, just as if you were calculating

manually. When a program is run, it uses the data already keyed into the

display and the registers inside the calculator.

3. Press t to begin program execution.

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Example: Run the program created above to calculate the net cost of a typewriter

listing for $625 and an executive chair listing for $159.

Keystrokes Display

fs 155.00 Sets calculator to Run mode. Display

shows number previously calculated.

625 625. Keys in price of typewriter.

t 473.75 Net cost of typewriter.

159 159. Keys in list price of chair.

t 124.25 Net cost of chair.

That’s all there is to creating and running simple programs! But if you want to use

programs frequently, you’ll want to know more about programming — such as

how to check what keystrokes are stored in program memory, how many

keystrokes can be stored in program memory, how to correct or otherwise modify

programs, how to skip keystrokes when running a program, and so on. Before you

can understand these aspects of programming, we need to briefly discuss how

keystrokes are treated by the calculator when they are stored in Program mode

and when they are executed in Run mode.

Program Memory

Keystrokes entered into the calculator in Program mode are stored in program

memory. Each digit, decimal point, or function key is called an instruction and is

stored in one line of program memory — usually referred to simply as a program

line. Keystroke sequences beginning with the f, g, ?, :, and i prefix

keys are considered to comprise a complete instruction and are stored in only one

program line.

When a program is run, each instruction in program memory is executed — that is,

the keystroke in that program line is performed, just as if you were pressing the key

manually — beginning with the current line in program memory and proceeding

sequentially with the higher-numbered program lines.

Whenever the calculator is in Program mode (that is, whenever the PRGM status

indicator in the display is lit), the display shows information about the program line

to which the calculator is currently set. At the left of the display is the number of the

program line within program memory. The remaining digits in the display comprise

a code that indicates what instruction has been stored in that program line. No

code is shown for program line 00, since no regular instruction is stored there.

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Identifying Instructions in Program Lines

Each key on the hp 12c keyboard — except for the digit keys 0 through 9 — is

identified by a two-digit “keycode” that corresponds to the key’s position on the

keyboard. The first digit in the keycode is the number of the key row, counting

from row 1 at the top; the second digit is the number of the key in that row,

counting from 1 for the first key in the row through 9 for the ninth key in the row

and 0 for the tenth key in the row. The keycode for each digit key is simply the

digit on the key. Thus, when you keyed the instruction b into program memory,

the calculator displayed

04– 25

This indicates that the key for the instruction in program line 04 is in the second

row on the keyboard and is the fifth key in that row: the b key. When you keyed

the instruction + into program memory, the calculator displayed

07– 40

This indicates that the key for the instruction in program line 07 is in the fourth row

on the keyboard and is the tenth key in that row: the + key. When you keyed the

digit 5 into program memory, the keycode displayed was only the digit 5.

Since keystroke sequences beginning with f, g, ?, :, and i are stored

in only one program line, the display of that line would show the keycodes for all

the keys in the keystroke sequence.

Instruction Keycode

gÒ nn- 43 26

?=1 nn- 44 40 1

gi00 nn- 43,33 00

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Displaying Program Lines

Pressing fs to set the calculator from Run mode to Program mode displays the

line number and keycode for the program line to which the calculator is currently

set.

Occasionally you’ll want to check several or all of the instructions stored in

program memory. The hp 12c enables you to review program instructions either

forward or backward through program memory:

z Pressing Ê (single step) while the calculator is in Program mode advances

the calculator to the next line in program memory, then displays that line

number and the keycode of the instruction stored there.

z Pressing gÜ (back step) while the calculator is in Program mode sets the

calculator back to the previous line in program memory, then displays that

line number and the keycode of the instruction stored there.

For example, to display the first two lines of the program now stored in program

memory, set the calculator to Program mode and press Ê twice:

Keystrokes Display

fs 00- Sets calculator to Program mode

and displays current line of

program memory

Ê 01- 36

Program line 01: \

Ê 02- 2

Program line 02: digit 2.

Pressing gÜ does the reverse:

Keystrokes Display

gÜ 01- 36

Program line 01.

gÜ 00- Program line 00.

If either the Ê key or the Ü key is held down, the calculator displays all of the

lines in program memory. Press Ê again now, but this time hold it down until

program line 07 is displayed.

Keystrokes Display

Ê 01- 36

Program line 01

.

.

.

.

.

.

(Release Ê) 07- 40

Program line 07

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Program line 07 contains the last instruction you keyed into program memory.

However, if you press Ê again, you’ll see that this is not the last line stored in

program memory:

Keystrokes Display

Ê 08- 43, 33 00 Program line 08

As you should now be able to tell from the keycodes displayed, the instruction in

program line 08 is gi00.

The 00 Instruction and Program Line 00

Whenever you run the program now stored in program memory, the calculator

executes the instruction in line 08 after executing the seven instructions you keyed

in. This i00 instruction — as its name implies — tells the calculator to “go to”

program line 00 and execute the instruction in that line. Although line 00 does not

contain a regular instruction, it does contain a “hidden” instruction that tells the

calculator to halt program execution. Thus, after each time the program is run, the

calculator automatically goes to program line 00 and halts, ready for you to key in

new data and run the program again. (The calculator is also automatically set to

program line 00 when you press fs to set the calculator from Program mode

to Run mode.)

The i00 instruction was already stored in line 08 — in fact, in all program

lines — before you keyed in the program. If no instructions have been keyed into

program memory, if Continuous Memory is reset, or if fCLEARÎ is pressed (in

Program mode), the instruction i00 is automatically stored in program lines 01

through 08. As you key each instruction into program memory, it replaces the

i00 instruction in that program line.

If your program should consist of exactly eight instructions, there would be no

i00 instructions remaining at the end of program memory. Nevertheless, after

such a program is executed the calculator automatically returns to program line 00

and halts, just as if there were a i00 instruction following the program.

If you key in more than eight instructions, program memory automatically expands

to accommodate the additional instructions.

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Expanding Program Memory

If no instructions have been keyed into program memory, if Continuous Memory

has been reset, or if fCLEARÎ has been pressed (in Program mode), program

memory consists of 8 program lines, and there are 20 storage registers available

for storage of data.

As you key in a ninth instruction, storage register R.9 is automatically converted into

seven new lines of program memory. The instruction you key in is stored in

program line 09, and the instruction i00 is automatically stored in program

lines 10 through 15.

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Program memory is automatically expanded like this whenever another seven

instructions have been keyed into program memory — that is, when you key an

instruction into program line 16, 23, 30 etc. In each case, the additional program

lines made available are converted, seven lines at a time, from the last available

data storage register (whether or not data has been stored in that register; if it has,

it will be lost). Furthermore, the six new program lines (following the 16th, 23th

etc.) will each contain the instruction i00.

To determine at any time how many program lines (including those containing

i00) are currently in program memory and how many storage registers are

currently available for conversion to program lines or for data storage, press

gN (memory). The calculator will respond with a display like the following:

Up to 99 instructions can be stored in program memory. Doing so would require

the conversion of 13 data storage registers (because 99 = 8 + [13 × 7]), leaving

7 storage registers — R0 through R6 — available for data storage.

If you find yourself creating long programs, you should create your programs so

that they don’t use up program lines unnecessarily, since program memory is

limited to 99 program lines. One way to minimize program length is to replace

numbers consisting of more than just one digit — like the number 25 in lines 02

and 03 of the program keyed in above — by a : instruction, and then storing

the number in the designated storage register before running the program. In this

case, this would save one program line, since the : instruction requires only

one program line, not two as are required by the number 25. Of course, doing so

uses up data storage registers that you might want to save for other data. As in

many business and financial decisions, there is a trade off involved; here it is

between program lines and data storage registers.

Setting the Calculator to a Particular Program Line

There will be occasions when you’ll want to set the calculator directly to a

particular program line — such as when you’re storing a second program in

program memory or when you’re modifying an existing program. Although you

can set the calculator to any line by using Ç as described above, you can do so

more quickly as follows:

z With the calculator in Program mode, pressing gi. followed by two

digit keys sets the calculator to the program line specified by the digit keys,

and then displays that line number and the keycode of the instruction stored

there.

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z With the calculator in Run mode, pressing gi followed by two digit keys

sets the calculator to the program line specified by the digit keys. Since the

calculator is not in Program mode, the line number and keycode are not

displayed.

The decimal point is not necessary if the calculator is in Run mode, but it is

necessary if the calculator is in Program mode.

For example, assuming the calculator is still in Program mode, you can set it to

program line 00 as follows:

Keystrokes Display

gi.00 00- Program line 00

Executing a Program One Line at a Time

Pressing Ç repeatedly with the calculator in Program mode (as described earlier)

enables you to verify that the program you have stored is identical to the program

you wrote — that is, to verify that you have keyed the instructions in correctly.

However, this does not ensure that the program you wrote calculates the desired

results correctly: even programs created by the most experienced programmers

often do not work correctly when they are first written.

To help you verify that your program works correctly, you can execute the program

one line at a time, using the Ç key. Pressing Ç while the calculator is in Run

mode advances the calculator to the next line in program memory, then displays

that line’s number and the keycode of the instruction stored there, just as in

Program mode. In Run mode, however, when the Ç key is released the

instruction in the program line just displayed is executed and the display then

shows the result of executing that line.

For example, to execute the program stored in the calculator one line at a time:

Keystrokes Display

fs 124.25 Sets calculator to Run mode and

to line 00 in program memory.

(Display shown assumes results

remain from previous

calculation.)

625 625. Keys in price of typewriter.

Ç 01- 36 Program line 01: \

625.00 Result of executin

g

pro

g

ram line

01.

Ç 02- 2 Program line 02: 2.

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Keystrokes Display

2. Result of executin

g

pro

g

ram line

02.

Ç 03- 5 Program line 03: 5.

25. Result of executin

g

pro

g

ram line

03.

Ç 04- 25 Program line 04: b

156.25 Result of executin

g

pro

g

ram line

04.

Ç 05- 30 Program line 05: -

468.75 Result of executin

g

pro

g

ram line

05.

Ç 06- 5 Program line 06: 5

5. Result of executin

g

pro

g

ram line

06.

Ç 07- 40 Program line 07: +

473.75 Result of executin

g

pro

g

ram line

07 (the last line of the program).

Pressing gÜ while the calculator is in Run mode sets the calculator to the

previous line in program memory, then displays that line’s number and the

keycode of the instruction stored there, just as in Program mode. In Run mode,

however, when the Ü key is released the display again shows the same number

as it did before gÜ was pressed: no instruction in program memory is

executed.

Interrupting Program Execution

Occasionally you’ll want a program to stop executing so that you can see an

intermediate result or enter new data. The hp 12c provides two functions for doing

so: u (pause) and t (run/stop).

Pausing During Program Execution

When a running program executes a u instruction, program execution halts for

about 1 second, then resumes. During the pause, the calculator displays the last

result calculated before the u instruction was executed.

If you press any key during a pause, program execution is halted indefinitely. To

resume program execution at the program line following that containing the u

instruction, press t.

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Example: Create a program that calculates the entries in the AMOUNT, TAX,

and TOTAL columns for each item on the jewelry distributor’s invoice shown on the

next page, and also calculates the total in each of these columns for all items on

the invoice. Assume the sales tax is 63/4%.

To conserve lines of program memory, instead of keying in the tax rate before the

b instruction we’ll store it in register R0 and recall it before the b instruction.

Before storing the program in program memory, we’ll calculate the required

amounts for the first item on the invoice manually. The keystroke sequence will use

storage register arithmetic (described on page 24) in registers R1, R2, and R3 to

calculate the column sums. Since these registers are cleared when fCLEAR² is

pressed, we’ll press those keys before beginning the manual calculation — and

also later, before running the program — to ensure that the column sums are

“initialized” to zero. (Pressing fCLEARH would clear registers R1 through R3,

but would also clear R0, which will contain the tax rate.)

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Pressing the gu keys is not necessary when we do the calculations manually,

since in Run mode the result of every intermediate calculation is displayed

automatically; but we’ll include u instructions in the program so that the

intermediate results AMOUNT and TAX are automatically displayed when the

program is executed.

Keystrokes Display

6.75?0 6.75 Stores tax rate in R0.

fCLEAR² 0.00 Clears the registers in R1 throu

g

h

R6.

13 13. Keys in quantity of item.

\ 13.00 Separates quantity of item from

cost of item to be keyed in next.

68.5 68.5 Keys in cost of item.

§ 890.50 AMOUNT.

?+1 890.50 Adds AMOUNT to sum of

AMOUNT entries in register R1.

:0 6.75 Recalls tax rate to display.

b 60.11 TAX.

?+2 60.11 Adds TAX to sum of TAX entries

in register R2.

+ 950.61 TOTAL.

?+3 950.61 Adds TOTAL to sum of TOTAL

entries in register R3.

Now, we’ll store the program in program memory. Do not key in the quantity and

cost of each item; these numbers will vary each time the program is run.

Keystrokes Display

fs 00- Sets calculator to Program

mode.

fCLEARÎ 00- Clears program memory.

§ 01- 20

gu 02- 43 31 Pauses to display AMOUNT.

?+1 03- 44 40 1

:0 04- 45 0

b 05- 25

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Keystrokes Display

gu 06- 43 31 Pauses to display TAX.

?+2 07- 44 40 2

+ 08- 40

?+3 09- 44 40 3

Now, to run the program:

Keystrokes Display

fs 950.61 Sets calculator to Run mode.

fCLEAR² 0.00 Clears registers R1– R6.

6.75?0 Stores tax rate.

13\68.5 68.5 Enters quantity and price of first

item on invoice.

t 890.50 AMOUNT for first item.

60.11 TAX for first item.

950.61 TOTAL for first item.

18\72.9 72.9 Enters quantity and price of

second item on invoice.

t 1,312.20 AMOUNT for second item.

88.57 TAX for second item.

1,400.77 TOTAL for second item.

24\85 85. Enters quantity and price of third

item on invoice.

t 2,040.00 AMOUNT for third item.

137.70 TAX for third item.

2,177.70 TOTAL for third item.

5\345 345. Enters quantity and price of

fourth item on invoice.

t 1,725.00 AMOUNT for fourth item.

116.44 TAX for fourth item.

1,841.44 TOTAL for fourth item.

:1 5,967.70 Sum of AMOUNT column.

:2 402.82 Sum of TAX column.

:3 6,370.52 Sum of TOTAL column.

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If the duration of the pause is not long enough to write down the number displayed,

you can prolong it by using more than one u instruction. Alternatively, you can

have the program automatically stop as described next.

Stopping Program Execution

Stopping Program Execution Automatically. Program execution is

automatically halted when the program executes a t instruction. To resume

executing the program from the program line at which execution was halted, press

t.

Example: Replace the program above by one containing t instructions

instead of u instructions.

Keystrokes Display

fs 00- Sets calculator to Program mode.

fCLEARÎ 00- Clears program memory.

§ 01- 20

t 02- 31 Stops program execution to display

AMOUNT.

?+1 03- 44 40 1

:0 04- 45 0

b 05- 25

t 06- 31 Stops program execution to display

TAX.

?+2 07- 44 40 2

+ 08- 40

?+3 09- 44 40 3

fs 6,370.52 Sets calculator to Run mode.

fCLEAR² 0.00 Clears registers R1 through R6.

13\68.5 68.5 First item.

t 890.50 AMOUNT for first item.

t 60.11 TAX for first item.

t 950.61 TOTAL for first item.

18\72.9 72.9 Second item.

t 1,312.20 AMOUNT for second item.

t 88.57 TAX for second item.

t 1,400.77 TOTAL for second item.

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Keystrokes Display

24\85 85. Third item.

t 2,040.00 AMOUNT for third item.

t 137.70 TAX for third item.

t 2,177.70 TOTAL for third item.

5\345 345. Fourth item.

t 1,725.00 AMOUNT for fourth item.

t 116.44 TAX for fourth item.

t 1,841.44 TOTAL for fourth item.

:1 5,967.70 Sum of AMOUNT column.

:2 402.82 Sum of TAX column.

:3 6,370.52 Sum of TOTAL column.

Program execution is also automatically halted when the calculator overflows (refer

to page 73) or attempts an improper operation that results in an Error display.

Either of these conditions signifies that the program itself probably contains an

error.

To determine at which program line execution has halted (in order to locate the

error), press any key to clear the Error display, then press fs to set the

calculator to Program mode and display that program line.

You may also want to display the current program line (by pressing fs) if

your program has halted at one of several t instructions in your program and

you want to determine which one that is. To continue executing the program

afterward:

1. Press fs to set the calculator back to Run mode.

2. If you want to resume execution from the program line at which execution

halted rather than from line 00, press gi followed by two digit keys that

specify the program line desired.

3. Press t to resume execution.

Stopping Program Execution Manually. Pressing any key while a program

is running halts program execution. You may want to do this if the calculated

results displayed by a running program appear to be incorrect (indicating that the

program itself is incorrect).

To halt program execution during a pause in a running program (that is, when

u is executed), press any key.

After stopping program execution manually, you can determine at which program

line execution has halted and/or resume program execution as described above.

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Section 9

Branching and Looping

Although the instructions in a program normally are executed in order of their

program line numbers, in some situations it is desirable to have program execution

transfer or “branch” to a program line that is not the next line in program memory.

Branching also makes it possible to automatically execute portions of a program

more than once — a process called “looping.”

Simple Branching

The i (go to) instruction is used in a program to transfer execution to any

program line. The program line desired is specified by keying its two-digit line

number into the program line containing the i instruction. When the i

instruction is executed, program execution branches or “goes to” the program line

specified and then continues sequentially as usual.

You have already seen a common use of branching: the i00 instruction (that is

stored in program memory after the program you key in) transfers execution to

program line 00. A i instruction can be used to branch not only backward in

program memory — as in the case of i00 and as illustrated above — but also

forward in program memory. Backward branching is typically done to create

loops (as described next); forward branching is typically done in conjunction with

an o or m instruction for conditional branching (as described afterward).

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Looping

If a i instruction specifies a lower-numbered line in program memory, the

instructions in the program lines between the specified line and the i instruction

will be executed repeatedly. As can be seen in the illustration above under Simple

Branching, once the program begins executing the “loop” it will execute it again

and again.

If you want to terminate the execution of a loop, you can include an o or m

instruction (described below) or an t instruction within the loop. You can also

terminate execution by pressing any key while the loop is being executed.

Example: The following program automatically amortizes the payments on a

home mortgage without requiring you to press f! for each payment. It will

amortize one month’s payments each time or one year’s payments each time the

loop is executed, depending on whether the number 1 or 12 is in the display

when you start running the program. Before running the program, we’ll “initialize”

it by storing the required data in the financial registers — just as we would do if

we were amortizing a single payment manually. We’ll run the program for a

$50,000 mortgage at 123/4% for 30 years, and we’ll key 1 into the display just

before running it in order to amortize monthly payments. For the first two “passes”

through the loop we’ll execute the program one line at a time, using Ç, so that

we can see the looping occurring; then we’ll use t to execute the entire loop a

third time before terminating execution.

Keystrokes Display

fs 00- Sets calculator to Program mode.

fCLEARÎ 00- Clears program memory

?0 01- 44 0 Stores the number from the display

into register R0. This number will be

the number of payments to be

amortized.

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Keystrokes Display

:0 02- 45 0 Recalls the number of payments to

be amortized. This program line is

the one to which pro

g

ram execution

will later branch. It is included

because after the first time the loop

is executed, the number in the

“display”* is replaced by the result

of !.

f! 03- 42 11 Amortizes payment(s).

gu 04- 43 31 Pauses to display amount of

payment(s) applied to interest.

~ 05- 34 Brings amount of payment(s)

applied to principal into “display.”*

gu 06- 43 31 Pauses to display amount of

payment(s) applied to principal.

gi02 07- 43, 33 02 Transfers program execution to line

02, so that the number of payments

to be amortized can be recalled to

the display before the !

instruction in line 03 is executed.

fs 0.00 Sets calculator to Run mode.

(Display shown assumes no results

remain from previous calculations.)

fCLEARG 0.00 Clears financial registers.

30gA 360.00 Enters n.

12.75gC 1.06 Enters i.

50000$ 50,000.00 Enters PV.

gÂ 50,000.00 Sets payment to End.

P –543.35 Calculates the monthly payment.

0n 0.00 Reset n to zero.

1 1. Keys 1 into the display to amortize

monthly payments.

Ê 01- 44 0 Line 01: ?0.

1.00

* More precisely, the number in the X-register.

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Keystrokes Display

Ê 02- 45 0 Line 02: :0. This is the be

g

innin

g

of the first pass through the loop.

1.00

Ê 03- 42 11 Line 03: f!.

–531.25 Portion of first month’s payment

applied to interest.

Ê 04- 43 31 Line 04: gu.

–531.25

Ê 05- 34 Line 05: ~.

–12.10 Portion of first month’s payment

applied to principal.

Ê 06- 43 31 Line 06: gu.

–12.10

Ê 07- 43, 33 02 Line 07: gi02. This is the end

of the first pass through the loop.

–12.10

Ê 02- 45 0 Line 02: :0. Program execution

has branched to the beginning of

the loop for the second pass throu

g

h

it.

1.00

Ê 03- 42 11 Line 03: f!.

–531.12 Portion of second month’s payment

applied to interest.

Ê 04- 43 31 Line 04: gu.

–531.12

Ê 05- 34 Line 05: ~.

–12.23 Portion of second month’s payment

applied to principal.

Ê 06- 43 31 Line 06: gu.

–12.23

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Keystrokes Display

Ê 07- 43, 33 02 Line 07: gi02.

This is the end of the second pass

through the loop.

–12.23

t –530.99 Portion of third month’s payment

applied to interest.

–12.36 Portion of third month’s payment

applied to principal.

t(or any key) –12.36 Halts program execution.

Conditional Branching

Often there are situations when it is desirable for a program to be able to branch

to different lines in program memory, depending on certain conditions. For

example, a program used by an accountant to calculate taxes might need to

branch to different program lines depending on the tax rate for the particular

income level.

The hp 12c provides two conditional test instructions that are used in programs for

conditional branching:

z o tests whether the number in the X-register (represented by the x in the

key symbol) is less than or equal to the number in the Y-register (represented

by the y in the key symbol). As discussed in Appendix A, the number in the

X-register is simply the number that would, if the calculator were in Run mode,

be currently in the display; and the number in the Y-register is the number

that would, if the calculator were in Run mode, have been in the display

when \ was pressed. For example, pressing 4\5 would place the

number 4 in the Y-register and the number 5 in the X-register.

z m tests whether the number in the X-register is equal to zero.

The possible results of executing either of these instructions are:

z If the condition tested for is true when the instruction is executed, program

execution continues sequentially with the instruction in the next line of

program memory.

z If the condition tested for is false when the instruction is executed, program

execution skips the instruction in the next line of program memory and

continues with the instruction in the following line.

These rules can be summarized as “DO if TRUE”.

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The program line immediately following that containing the conditional test

instruction can contain any instruction; however, the most commonly used

instruction there is i. If a i instruction follows a conditional test instruction,

program execution branches elsewhere in program memory if the condition is true

and continues with the next line in program memory if the condition is false.

Example: The following program calculates income tax at a rate of 20% on

incomes of $20,000 or less and 25% on incomes of more than $20,000. To

conserve program lines, the program assumes that the test value — 20,000 — has

been stored in register R0 and the tax rates — 20 and 25 — have been stored in

registers R1 and R2, respectively.

Note: If a program requires that certain numbers be in the X- and

Y-registers when instructions such as o are executed, it is extremely helpful

when writing the program to show the quantities in each register after each

instruction is executed, as in the following diagram.

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We’ll key the income into the display before running the program so that it will be

in the X-register when the :0 instruction in program line 01 is executed. This

instruction will place the test value 20,000 in the X-register and (as explained in

Appendix A) move the income into the Y-register. The ~ instruction in program

line 02 will exchange the numbers in the X- and Y-registers (as also explained in

Appendix A): that is, it will place the income back into the X-register and place the

test value into the Y-register. This is necessary because when either the :2

instruction in line 05 or the :1 instruction in line 07 is executed, the number in

the X-register is moved into the Y-register; if the ~ instruction were not included,

the test value 20,000, rather than the income, would be in the Y-register when the

b instruction in line 08 is executed.

Keystrokes Display

fs 07- 43, 33 02 Sets calculator to Program mode.

(Display shows program line at

which execution was halted at end

of preceding example.)

fCLEARÎ 00- Clears program memory.

:0 01- 45 0 Recalls test value into X-register and

places income in Y-register.

~ 02- 34 Places income in X-register and test

value in Y-register.

go 03- 43 34 Tests whether number in X-register

(income) is less than or equal to

number in Y-register (20,000).

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Keystrokes Display

gi07 04- 43, 33 07 If condition is true, branches to

program line 07.

:2 05- 45 2 If condition is false, recalls 25% tax

rate to X-register.

gi08 06- 43, 33 08 Branches to program line 08.

:1 07- 45 1 Recalls 20% tax rate to X-register.

b 08- 25 Calculates tax.

fs –12.36 Sets calculator to Run mode.

(Display shows results of running of

previous program.)

Now, we'll store the required numbers in registers R0, R1, and R2, then we’ll run the

program, using Ç so that we can check that the branching occurs properly. It’s

good practice with programs containing conditional test instructions to check that

the program branches correctly for all possible conditions: in this case, if the

income is less than, equal to, or greater than the test value.

Keystrokes Display

20000?0 20,000.00 Stores test value in register R0.

20?1 20.00 Stores 20% tax rate in register R1.

25?2 25.00 Stores 25% tax rate in register R2.

15000 15,000. Keys income less than test value into

display and X-register.

Ê 01- 45 0 Line 01: :0.

20,000.00 Test value has been recalled to

X-register, moving income to

Y-register.

Ê 02- 34 Line 02: ~

15,000.00 Income has been placed in

X-register and test value has been

placed in Y-register.

Ê 03- 43 34 Line 03: go

15,000.00

Ê 04- 43, 33 07 Condition tested by o was true,

so program execution continued

with line 04: gi07.

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Keystrokes Display

15,000.00

Ê 07- 45 1 Line 07: :1.

20.00 20% tax rate has been recalled to

X-register, moving income to

Y-register.

Ê 08- 25 Line 08: b.

3,000.00 20% of 15,000 = 3,000.

20000 20,000. Keys income equal to test value into

display and X-register.

Ê 01- 45 0 Line 01: :0.

20,000.00 Test value has been recalled to

X-register, moving income to

Y-register.

Ê 02- 34 Line 02: ~.

20,000.00 Income has been placed in

X-register and test value has been

placed in Y-register.

Ê 03- 43 34 Line 03 go.

20,000.00

Ê 04- 43, 33 07 Condition tested by o was true,

so program execution continued

with line 04: gi07.

20,000.00

Ê 07- 45 1 Line 07: :1.

20.00 20% tax rate has been recalled to

X-register, moving income to

Y-register.

Ê 08- 25 Line 08: b.

4,000.00 20% of 20,000 = 4,000.

25000 25,000. Keys income greater than test value

into display and X-register.

Ê 01- 45 0 Line 01: :0.

20,000.00 Test value has been recalled to

X-register, moving income to

Y-register.

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Keystrokes Display

Ê 02- 34 Line 02: ~.

25,000.00 Income has been placed in

X-register and test value has been

placed in Y-register.

Ê 03- 43 34 Line 03: go.

25,000.00

Ê 05- 45 2 Condition tested by o was false,

so program execution skipped the

next line and continued at line 05:

:2.

25.00 25% tax rate has been recalled to

X-register, moving income to

Y-register.

Ê 06- 43, 33 08 Line 06: gi08.

25.00

Ê 08- 25 Line 08: b.

6,250.00 25% of 25,000 = 6,250.

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Section 10

Program Editing

There are various reasons why you might want to modify a program you have

stored in Program memory: to correct a program that turns out to have errors; to

insert new instructions such as ? to store intermediate results or u to display

intermediate results; or to replace a u instruction by an t instruction.

Rather than clearing program memory and keying in the modified program, you

can modify the program already stored in the calculator. This is called program

editing.

Changing the Instruction in a Program Line

To change a single instruction in program memory:

1. Press fs to set the calculator to Program mode.

2. Use Ç, Ü, or i. to set the calculator to the program line preceding

the line containing the instruction to be changed.

3. Key in the new instruction.

For example, to change the instruction stored in program line 05, press

gi.04, then key in the new instruction that is to be stored in program line

05. The instruction previously stored in line 05 will be replaced; it is not

automatically “bumped” into line 06.

Example: With the last program from the preceding section still stored in the

calculator, suppose you wanted to use register R2 for some other purpose, and so

you needed to replace the :2 instruction in program line 05 with, say, :6.

You could change the instruction in line 05 as follows:

Keystrokes Display

fs 00- Sets calculator to Program mode.

gi.04 04- 43, 33 07 Sets calculator to program line

preceding that containing the instruction

to be changed.

:6 05- 45 6 Keys new instruction into program line

05, replacing the :2 instruction

previously there.

Ê 06- 43, 33 08 Shows that instruction in program line

06 has not been changed.

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Keystrokes Display

fs 6,250.00 Sets calculator back to Run mode.

(Display shown assumes results remain

from last example in precedin

g

section.)

:2?6 25.00 Copies tax rate from R2 into R6.

Adding Instructions at the End of a Program

To add one or more instructions at the end of the last program stored in program

memory:

1. Press fs to set the calculator to Program mode.

2. Press gi. followed by two digits that specify the last line you keyed

into program memory (that is, the highest numbered line, not necessarily the

line most recently keyed in).

3. Key in the new instruction or instructions.

Note: To add one or more instructions at the end of a program that is not

the last program stored in program memory, use the procedure described

below under Adding Instructions Within a Program.

Example: With the last program from the preceding section stored in the

calculator, suppose you wanted to add a - instruction at the end in order to

calculate the net income after taxes. You could do so as follows:

Keystrokes Display

fs 00- Sets calculator to Program mode.

gi.08 08- 25 Sets calculator to last line keyed into

program memory.

- 09- 30 Keys new instruction into program

line 09.

fs 25.00 Sets calculator back to Run mode.

15000t 12,000.00 Net income after 20% tax is

subtracted from $15,000 income.

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Adding Instructions Within a Program

If an instruction is to be added within a program, simply keying it in will replace

the instruction previously stored in that program line, as described above; the

contents of all higher-numbered program lines remain unchanged.

To add instructions within a program, you could simply key in the new instructions,

beginning at the proper program line, followed by the original instructions from

that program line through the end of the program. This method is described below

under Adding Instructions by Replacement. When instructions must be added in the

middle of a long program, however, using this method will require you to key in

numerous instructions — namely, the original instructions from the point at which

the new instructions are added through the end of program memory. Since keying

in these instructions may require a significant amount of time, in such situations you

may prefer to use the method described below under Adding Instructions by

Branching.

That method basically involves branching to the new instructions which are stored

at the end of program memory, then branching back to the program line

immediately following the line from which you branched out. Adding instructions

by branching is not so simple as adding instructions by replacement; however, it

generally will require fewer keystrokes whenever there are more than four program

lines between (and including) the first line to be executed after the new instruction(s)

and the last line you keyed into program memory. Furthermore, if program

memory includes branches to program lines following the point at which the new

instruction(s) are being added, adding instructions by branching will not require

that you change the line numbers specified in the i instructions, which may be

necessary when you add instructions by replacement.

Adding Instructions by Replacement

1. Press fs to set the calculator to Program mode.

2. Press gi. followed by two digits that specify the last program line to

be executed before the added instruction(s). This sets the calculator to the

proper program line for adding the new instruction(s) in the next step.

3. Key in the new instruction or instructions.

4. Key in the original instruction or instructions, beginning with the first

instruction to be executed after the added instruction(s), and continuing

through the last instruction you keyed into program memory.

Note: If program memory includes branches to program lines following that

at which the first new instruction is being added, remember to change the

line number(s) specified in the i instruction(s) — as described above

under Changing the Instruction in a Program Line — to the actual new line

number(s).

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Example: Assuming you have added a - instruction at the end of program

memory as in the preceding example, suppose you now wanted to insert an t

instruction before the - instruction so that the program will display the amount of

the tax before displaying the net income after tax. Since there is only one

instruction (-) following the point at which the new instruction is being added, it

is simplest to add the t instruction by replacement, as follows:

Keystrokes Display

fs 00- Sets calculator to Program mode.

gi.08 08- 25

Sets calculator to last pro

g

ram line

to be executed, which contains the

b instruction.

t 09- 31

Keys in new instruction.

- 10- 30

Keys in original instruction, which

was replaced by new instruction

added.

fs 12,000.00 Sets calculator back to Run mode.

15000t 3,000.00 Twenty percent tax on $15,000

income.

t 12,000.00 Net income after tax.

Adding Instructions by Branching

1. Press fs to set the calculator to Program mode.

2. Press gi. followed by two digits that specify the program line

immediately preceding the point at which the new instruction(s) are being

added — usually, the last program line to be executed before the added

instruction(s). This sets the calculator to the proper program line for inserting

a i instruction in the next step. This i instruction will replace whatever

instruction was already stored there, but that instruction will be keyed back

into program memory, to be executed just after the new instructions, in step

7.

3. Press gi followed by two digits that specify the second line after the last

line you keyed into program memory. (Branching to the second line rather

than to the first is necessary because the first line following the last program

in program memory must contain a i00 instruction. The i00

instruction ensures that program execution will branch to line 00 and halt

after the program is run.) For example, if the last line you keyed into

program memory was line 10, you would press gi12 at this step,

preserving the gi00 in line 11.

4. Press gi. followed by two digits that specify the last line you keyed

into program memory.

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5. Press gi00. This automatically converts a data storage register into

seven additional lines of program memory (if there was not already a

i00 instruction remaining at the end of program memory), and it ensures

that program execution will branch to line 00 after the program is run.

6. Key in the instruction(s) being added.

7. Key in the instruction that originally immediately followed the point at which

the new instruction(s) are being added — that is, the first instruction to be

executed after the added instruction(s). (This instruction was replaced by the

i instruction keyed in at step 3.)

8. Press gi followed by two digits that specify the second line following

the point at which the new instruction(s) are being added. This i

instruction will cause program execution to branch back to the proper line

within the original program.

Example: Continuing with the preceding example, suppose incomes less than or

equal to $7,500 were not to be taxed. You could modify the program to check for

this condition and stop at line 00, displaying the original income keyed in, by

storing 7,500 in register R3 and adding the following instructions between lines 00

and 01: :3~gogi00. Since there are more than four instructions

between (and including) the first line to be executed after the added instructions

(line 01) and the last line you keyed into program memory (line 10), it will require

fewer keystrokes to add the new instructions by branching than to add them by

replacement.

Keystrokes Display

fs 00- Sets calculator to Program mode.

gi.00 00- Sets calculator to program line

immediately preceding point at

which new instructions are being

added. (In this particular example,

this step could have been skipped

since calculator was already set at

the proper program line.)

gi12 01- 43, 33 12 Branches to program line 12, the

second line after last line of

program.

gi.10 10- 30

Sets calculator to last line of

program so that i00 instruction

keyed in next will be stored in first

line following program.

gi00 11- 43, 33 00 Ensures that i00 instruction

follows program.

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Keystrokes Display

:3 12- 45 3

~ 13- 34

go 14- 43 34

gi00 15- 43, 33 00

Added instructions.

:0 16- 45 0

Keys in instruction immediately

following point at which new

instructions are being added. (This

instruction was replaced in line 01

by i12 instruction.)

gi02 17- 43, 33 02 Branches back to second line (line

02) following point at which new

instructions are being added.

fs 12,000.00 Sets calculator back to Run mode.

7500?3 7,500.00 Stores test value in register R3.

6500t 6,500.00 Runs program for income less than

$7,500. Display shows original

income keyed in, indicating that tax

is zero.

15000t 3,000.00 Tax on $15,000 income.

t 12,000.00 Net income after tax. This shows

program still works for an income

greater than $7,500 and less than

$20,000.

The following illustration of the edited program shows how program execution

branches to the instructions added at the end of program memory, then branches

back.

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Section 11

Multiple Programs

You can store multiple programs in program memory, provided that you separate

them by instructions that will halt program execution after each program is run and

return to the beginning of the program if it is run again. You can run programs

after the first one stored in program memory by setting the calculator to the first

line of the program using i before pressing t.

Storing Another Program

To store a program after another program is already stored in program memory:

1. Press fs to set the calculator to Program mode. Do not clear program

memory.

2. Press gi. followed by two digits that specify the number of the last

line you keyed into program memory.

Note: If this is the second program to be stored in program memory, you

will need to ensure that a i00 instruction separates it from the first

program by doing step 3. If there are already two or more programs stored

in program memory, skip step 3 and proceed with step 4.

3. Press gi00. This automatically converts a data storage register into

seven additional lines of program memory (if there was not already a