HP 12c_user's Guide_English_HDPMBF12E44 Guide_English_E_HDPMBF12E44 C00363319

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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.
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 $5,000 insurance policy that pays 5.35% annually, compounded
semiannually. How much would it be worth by the time she enters college?
In this example, we need to calculate FV, the future value.
Keystrokes Display
fCLEARG -21,396.61 Clears previous financial data inside
the calculator.
14\2µn 28.00 Calculates and stores the number of
compounding periods.
5.35\2 2.68 Calculates and stores the periodic
interest rate.
5000Þ$ -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.
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:
22 Section 1: Getting Started
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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 . 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 . 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
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 .
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
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.
10.142005 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 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.
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 if payments are made at the beginning of the compounding
periods.
z Press 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 or 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).
–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 $4000?
Keystrokes Display
fCLEARG
6.25\24
0.26
Calculates and stores i.
775Þ$ –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.
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 or 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 or 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).
–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.
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 or 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.
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 $3,200 and
intend to make semiannual deposits, beginning six months later, from your
profit-sharing bonus paychecks. Calculate how much these deposits should be.
Keystrokes Display
fCLEARG
15\2µw
30.00
Calculates and stores n.
9.75\2 4.88 Calculates and stores i.
3200Þ$ –3200.00 Stores PV (with minus sign for cash
paid out).
60000M 60,000.00 Stores FV.
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 or 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).
–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).
–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 . Pressing 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 $4,500 accrues interest at a 15% annual
percentage rate (APR), with the payments made at the end of each month. If
interest begins accruing on this loan on February 15, 2004 (so that the first period
begins on March 1, 2004), calculate the monthly payment, with the odd days
counted on the basis of a 30-day month and compound interest used for the odd
period.
Keystrokes Display
fCLEARG Clears financial registers.
Sets date format to month-day-year.
Sets payment mode to End.
Turns on the
Cindicator in the display,
so that compound interest will be used
for the odd period.
2.152004\ 2.15 Keys in the date interest begins
accruing and separates it from the
next date entered.
3.012004 3.012004 Keys in the date of the beginning of
the first period.
15.00 Actual number of odd days.
~ 16.00 Number of odd days counted on the
basis of a 30-day month.
30z 0.53 Divides by the length of a monthly
period to get the fractional part of n.
36+n 36.53 Adds the fractional part of n to the
number of complete payment periods,
then stores the result in n.
15gC 1.25 Calculates and stores i.
4500$ 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 $120 are
made at the end of each month. Calculate the annual percentage rate (APR), using
the actual number of odd days and simple interest for the odd period.
Keystrokes Display
fCLEARG Clears financial registers.
Turns off the Cindicator in the display,
so that simple interest will be used for
the odd period.
7.192004\ 7.19 Keys in the date interest begins
accruing and separates it from the
next date entered.
8.012004 8.012004 Keys in the date of the beginning of
the first period.
13.00 Actual number of odd days.
30z 0.43 Divides by the length of a monthly
period to get the fractional part of n.
42+n 42.43 Adds the fractional part of n to the
number of complete payment periods,
then stores the result in n.
3950$ 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 $.
4. Key in the periodic payment, then press ÞP (the sign of PMT must be
negative, in accordance with the cash flow sign convention).
5. Press or (for most direct reduction loans) to set the payment
mode.
6. Key in the number of payments to be amortized.
7. Press
f! to display the amount from those payments applied toward
interest.
8. Press ~ to display the amount from those payments applied toward the
principal.
9. To display the number of payments just amortized, press dd.
10. To display the remaining balance of the loan, press :$.
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).
–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 CFjstore 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.
Section 4: Additional Financial Functions 67
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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.
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 $.
2. Enter the annual coupon rate (as a percentage), using P.
3. Key in the settlement (purchase) date, then press \.
4. Key in the maturity (redemption) date.
5. Press fS.
The yield to maturity is shown in the display and also is stored in the i register.
Note: Remember that the S function may take a significant amount of
time to produce an answer, during which the calculator displays running.
68 Section 4: Additional Financial Functions
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Example: The market is quoting 883/8% for the bond described in the preceding
example. What yield will that provide?
Keystrokes Display
3\8z 0.38 Calculates 3/8.
88+$ 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 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 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.
21,714.29 Mean dollar sales per month ( x).
~ 40.00 Mean workweek in hours ( y).
Section 6: Statistics Functions 79
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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
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 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 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.
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
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 (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 does the reverse:
Keystrokes Display
01- 36
Program line 01.
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
pro
ram line
01.
Ç 02- 2 Program line 02: 2.
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Keystrokes Display
2. Result of executin
pro
ram line
02.
Ç 03- 5 Program line 03: 5.
25. Result of executin
pro
ram line
03.
Ç 04- 25 Program line 04: b
156.25 Result of executin
pro
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
pro
ram line
06.
Ç 07- 40 Program line 07: +
473.75 Result of executin
pro
ram line
07 (the last line of the program).
Pressing 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 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.
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).
110 Section 9: Branching and Looping
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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.
Section 9: Branching and Looping 111
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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.
112 Section 9: Branching and Looping
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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.
114 Section 10: Program Editing
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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.
118 Section 10: Program Editing
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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