Texas Instruments BA II PLUS User Manual

BA II PLUS™

Calculator

Important Information

Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

USA FCC Information Concerning Radio Frequency Interference

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation.

If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures:

• Reorient or relocate the receiving antenna.

• Increase the separation between the equipment and receiver.

• Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.

• Consult the dealer or an experienced radio/television technician for help.

Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment.

Contents

Important Information................................................................... ii

USA FCC Information Concerning Radio Frequency Interferenceii

1 Overview of Calculator Operations..................................1

Turning On the Calculator ............................................................. 1

Turning Off the Calculator............................................................. 1

Selecting 2nd Functions ................................................................. 2

Reading the Display ....................................................................... 2

Setting Calculator Formats ........................................................... 4

Resetting the Calculator ................................................................ 6

Clearing Calculator Entries and Memories ................................... 6

Correcting Entry Errors................................................................... 7

Math Operations ............................................................................ 8

Memory Operations ..................................................................... 12

Calculations Using Constants....................................................... 13

Last Answer Feature..................................................................... 14

Using Worksheets: Tools for Financial Solutions ........................ 15

2 Time-Value-of-Money and Amortization Worksheets...21

TVM and Amortization Worksheet Variables............................. 22

Entering Cash Inflows and Outflows........................................... 25

Generating an Amortization Schedule ....................................... 25

Example: Computing Basic Loan Interest.................................... 26

Examples: Computing Basic Loan Payments ............................... 27

Examples: Computing Value in Savings ...................................... 28

Example: Computing Present Value in Annuities....................... 29

Example: Computing Perpetual Annuities.................................. 30

Example: Computing Present Value of Variable Cash Flows ..... 31

Example: Computing Present Value of a Lease With Residual

Value........................................................................................ 33

Example: Computing Other Monthly Payments......................... 34

Example: Saving With Monthly Deposits.................................... 35

Example: Computing Amount to Borrow and Down Payment. 36 Example: Computing Regular Deposits for a Specified Future

Amount ................................................................................... 37

Example: Computing Payments and Generating an Amortization

Schedule .................................................................................. 38

Example: Computing Payment, Interest, and Loan Balance After

a Specified Payment ............................................................... 39

3 Cash Flow Worksheet......................................................41

Cash Flow Worksheet Variables................................................... 41

iii

Uneven and Grouped Cash Flows................................................42

Entering Cash Flows......................................................................43

Deleting Cash Flows......................................................................43

Inserting Cash Flows .....................................................................44

Computing Cash Flows .................................................................44

Example: Solving for Unequal Cash Flows ..................................46

Example: Value of a Lease with Uneven Payments ....................48

4 Bond Worksheet ............................................................. 51

Bond Worksheet Variables...........................................................52

Bond Worksheet Terminology .....................................................54

Entering Bond Data and Computing Results ..............................54

Example: Computing Bond Price and Accrued Interest..............56

5 Depreciation Worksheet ................................................ 57

Depreciation Worksheet Variables ..............................................57

Entering Data and Computing Results........................................59

Example: Computing Straight-Line Depreciation.......................61

6 Statistics Worksheet ....................................................... 63

Statistics Worksheet Variables .....................................................63

Regression Models........................................................................65

Entering Statistical Data...............................................................66

Computing Statistical Results.......................................................67

7 Other Worksheets ........................................................... 69

Percent Change/Compound Interest Worksheet ........................69

Interest Conversion Worksheet....................................................72

Date Worksheet............................................................................74

Profit Margin Worksheet .............................................................76

Breakeven Worksheet ..................................................................78

Memory Worksheet......................................................................80

A Appendix — Reference Information.............................. 83

Formulas........................................................................................83

Error Messages..............................................................................94

Accuracy Information ...................................................................95

AOS™ (Algebraic Operating System) Calculations.....................96

Battery Information......................................................................97

In Case of Difficulty ......................................................................98

Texas Instruments Support and Service ....................................... 99

Texas Instruments (TI) Warranty Information ........................... 100

Index ............................................................................... 103

Overview of Calculator Operations

This chapter describes the basic operation of your BA II PLUS™ calculator, including how to:

• Turn on and turn off the calculator

• Select second functions

• Read the display and set calculator formats

• Clear the calculator and correct entry errors

• Perform math and memory operations

• Use the Last Answer feature

• Use worksheets

Turning On the Calculator

Press $.

• If you turned off the calculator by pressing $, the calculator returns to the standard-calculator mode with a displayed value of zero.

All worksheets and formats for numbers, angle units, dates, separators, and calculation method retain previous values and configurations.

• If the Automatic Power Down™ (APD™) feature turned off the calculator, the calculator turns on exactly as you left it, saving display settings, stored memory, pending operations, and error conditions.

Turning Off the Calculator

Press $.

• The displayed value and any error condition clear.

• Any unfinished standard-calculator operation and worksheet calculation in progress cancel.

Overview of Calculator Operations 1

• The Constant Memory™ feature retains all worksheet values and settings, including the contents of the 10 memories and all format settings.

Automatic Power Down™ (APD™) Feature

To prolong battery life, the Automatic Power Down (APD) feature turns off the calculator automatically after about five minutes of inactivity.

The next time you press $, the calculator turns on exactly as you left it, saving display settings and stored memory and any pending operations or error conditions.

Selecting 2nd Functions

The primary function of a key is printed on the key itself. For example, the primary function of the $ key is to turn on or turn off the calculator.

Most keys include a second function printed above the key. To select a second function, press & and the corresponding key. (When you press &, the 2nd indicator appears in the upper left corner of the display.)

For example, pressing & U exits the selected worksheet and returns the calculator to the standardcalculator mode.

Note: To cancel after pressing &, press & again.

Reading the Display

The display shows the selected variable labels with values up to 10 digits. (The calculator displays values exceeding 10 digits in scientific notation.)

2 Overview of Calculator Operations

The indicators along the top of the display tell you which keys are active and offer information about the status of the calculator.

Indicator Meaning

2nd Press a key to select its second function.

INV Press a key to select its inverse trigonometric function.

HYP Press a key to select its hyperbolic function.

COMPUTE Press % to compute a value for the displayed variable.

ENTER Press ! to assign the displayed value to the displayed

variable.

SET

# $

DEL Press & W to delete a cash flow or statistical data point.

INS Press & X to insert a cash flow or statistical data point.

BGN TVM calculations use beginning-of-period payments. When

RAD Angle values appear in radians. When





= The displayed variable is assigned the displayed value.

– The displayed value is negative.

Press & V to change the setting of the displayed variable.

Press " or # to display the previous or next variable in the worksheet.

Note: To easily scroll up or down through a range of variables, press and hold # or ".

BGN is not displayed, TVM calculations use end-of-period

payments (END).

RAD is not displayed,

angle values appear and must be entered in degrees.

The displayed value is entered in the selected worksheet. The indicator clears following a computation.

The displayed value is computed in the selected worksheet. When a value changes and invalidates a computed value, the_indicator clears.

Overview of Calculator Operations 3

Setting Calculator Formats

You can change these calculator formats:

To Select Press Display Default

Number of decimal

& | DEC 0–9 (Press 9 for

floating-decimal)

places

Angle units # DEG (degrees)

RAD (radians)

Dates # US (mm-dd-yyyy)

Eur (dd-mm-yyyy)

Number separators

Calculation method

# US (1,000.00 )

Eur (1.000,00)

# Chn (chain)

AOSé (algebraic

operating system)

1. To access format options, press & |. The DEC indicator appears with the selected number of decimal places.

2. To change the number of decimal places displayed, key in a value and press !.

3. To access another calculator format, press # or " once for each format.

For example, to access the angle unit format, press #. To access the number-separator format, press "" "or # # #.

4. To change the selected format, press & V.

5. To change another calculator format, repeat step 3 and step 4. — or — To return to the standard-calculator mode, press & U. — or — To access a worksheet, press a worksheet key or key sequence.

DEG

Chn

Choosing the Number of Decimal Places Displayed

The calculator stores numeric values internally to an accuracy of 13 digits, but you can specify the number of decimal places you want to display. The calculator displays up to 10 digits with the floating-decimal option. Results exceeding 10 digits appear in scientific notation.

4 Overview of Calculator Operations

Changing the number of decimal places affects the display only. Except for amortization and depreciation results, the calculator does not round internal values. To round the internal value, use the round function.

Note: All examples in this guidebook assume a setting of two decimal places. Other settings might show different results.

Choosing the Angle Units

The angle unit value affects the display of results in trigonometric calculations. When you select radians, the RAD indicator appears in the upper right corner of the display. No indicator appears when you select the default setting of degrees.

Using Dates

The calculator uses dates with the Bond and Date worksheets and the French depreciation methods. To enter dates, use this convention: mm.ddyy (US) or dd.mmyy (European). After you key in the date, press !.

Choosing Calculation Methods

When you choose the chain (Chn) calculation method, the calculator solves problems in the order that you enter them. (Most financial calculators use Chn.)

For example, when you enter 3 H 2 < 4 N, the Chn answer is 20 (3 + 2 = 5, 5 * 4 = 20).

Using AOSé (algebraic operating system), the calculator solves problems according to the standard rules of algebraic hierarchy, computing multiplication and division operations before addition and subtraction operations. (Most scientific calculators use AOS.)

For example, when you enter 3 H 2 < 4 N, the AOS answer is 11 (2 Q 4 = 8; 3 + 8 = 11).

Resetting Default Values

To reset default values for all of the calculator formats, press & z with one of the formats displayed.

Overview of Calculator Operations 5

Resetting the Calculator

Resetting the calculator:

• Clears the display, all 10 memories, any unfinished calculations, and all worksheet data.

• Restores all default settings

• Returns operation to the standard-calculator mode

Because the calculator includes alternative methods that let you clear data selectively, use reset carefully to avoid losing data needlessly. (See “Clearing Calculator Entries and Memories

For example, you might reset the calculator before using it for the first time, when starting a new calculation, or when having difficulty operating the calculator and other possible solutions do not work. (See “In Case of Difficulty

” on page 98.)

Pressing & } !

1. Press & }. The

Note: To cancel reset, press & U. 0.00 appears.

2. Press !. RST and 0.00 appear, confirming that the calculator is reset.

Note: If an error condition exists, press P to clear the display before attempting to reset.

RST ? and ENTER indicators appear.

” on page 6.)

Performing a Hard Reset

You can also reset the calculator by gently inserting a pointed object (such as an unfolded paper clip or similar object) in the hole marked RESET in back of the calculator.

Clearing Calculator Entries and Memories

Note: To clear variables selectively, see the specific worksheet chapters in this guidebook.

To clear Press

One character at a time, starting with the last digit keyed in

An incorrect entry, error condition, or error message

6 Overview of Calculator Operations

To clear Press

The prompted worksheet and reset default values & z

Calculator format settings and reset default values & |

& z

• Out of the prompted worksheet and return to

& U

standard-calculator mode

• All pending operations in standard-calculator mode

• In a prompted worksheet, the variable value

P P

keyed in but not entered (the previous value appears)

• Any calculation started but not completed

TVM worksheet variables and reset default values & U

& ^

One of the 10 memories (without affecting the others)

Q D and a memory number key (0–9)

Correcting Entry Errors

You can correct an entry without clearing a calculation, if you make the correction before pressing an operation key (for example, H or 4).

• To clear the last digit displayed, press *.

• To clear the entire number displayed, press P.

Note: Pressing P after you press an operation key clears the calculation in progress.

Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86.

To Press Display

Begin the expression. 3 <

Enter a number.

1234.86 1,234.86

Erase the entry error. * *

Key in the correct number.

56 1,234.56

Compute the result. N

3.00

1,234.

3,703.68

Overview of Calculator Operations 7

Math Operations

When you select the chain (Chn) calculation method, the calculator evaluates mathematical expressions (for example, 3 + 2 Q 4) in the order that you enter them.

Examples of Math Operations

These operations require you to press N to complete.

To Press Display

Add 6 + 4

6 H 4 N

Subtract 6 N 4 6 B 4 N

Multiply 6 Q 4 6 < 4 N

Divide 6 P 4 6 6 4 N

Find universal power: 3

1.25

3 ; 1.25 N

Use parentheses: 7 Q (3 + 5) 7 < 9 3 H 5 : N

Find percent: 4% of $453 453 < 4 2 N

Find percent ratio: 14 to 25 14 6 25 2 N

Find price with percent add-on: $498 + 7% sales tax

Find price with percent discount: $69.99 N 10%

Find number of combinations where:

498 H 7 2

69.99 B 10 2

52 & s 5 N

n = 52, r = 5

Find number of permutations where:

8 & m 3 N

n = 8, r = 3

2,598,960.00

10.00

2.00

24.00

1.50

3.95

56.00

18.12

56.00

34.86

532.86

7.00

62.99

336.00

These operations do not require you to press N to complete.

To Press Display

Square 6.3

Find square root:

15.5

6.3 4

15.5 3

Find reciprocal: 1/3.2 3.2 5

Find factorial: 5! 5 & g

Find natural logarithm: ln 203.45 203.45 >

8 Overview of Calculator Operations

39.69

3.94

0.31

120.00

5.32

To Press Display

Find natural antilogarithm: e

.69315

.69315 & i

Round 2 P 3 to the set decimal format 2 6 3 N & o

Generate random number* & a

Store seed value D & a

Find sine:** sin(11.54°) 11.54 & d

Find cosine:** cos(120°) 120 & e

Find tangent:** tan(76°) 76 & f

Find arcsine:** sin-1(.2)

Find arccosine:** cos-1(-.5)

Find arctangent:** tan-1(4)

.2 8 d

.5 S 8 e

4 8 f

Find hyperbolic sine: sinh(.5) .5 & c d

Find hyperbolic cosine: cosh(.5) .5 & c e

Find hyperbolic tangent: tanh(.5) .5 & c f

Find hyperbolic arcsine: sinh-1(5)

Find hyperbolic arccosine: cosh-1(5)

Find hyperbolic arctangent: tanh-1(.5)

5 & c 8 d

5 & c 8 e

.5 & c 8 f

2.00

0.67

0.86

0.20

-0.50

4.01

11.54

120.00

75.96

0.52

1.13

0.46

2.31

2.29

0.55

* The random number you generate might be different.

** Angles can be computed in degrees or radians. Examples show

angles in degrees. (See “Choosing the Angle Units” on page 5.)

Universal Power ;

Press ; to raise the displayed positive number to any power (for example, 2

Note: Because the reciprocal of an even number (such as, 1/2, 1/4, 1/6) is a complex number, you can only raise a negative number to an integer power or the reciprocal of an odd number.

Overview of Calculator Operations 9

-5

or 2

(1/3)

Parentheses 9 :

Use parentheses to control the order in which the calculator evaluates a numeric expression in division, multiplication, powers, roots, and logarithm calculations. The calculator includes up to 15 levels of parentheses and up to 8 pending operations.

Note: You do not have to press : for expressions ending in a series of closed parentheses. Pressing N closes parentheses automatically, evaluates the expression, and displays the final result. To view intermediate results, press : once for each open parenthesis.

Factorial & g

The number for which you compute a factorial must be a positive integer less than or equal to 69.

Random Numbers & a

The calculator generates a random real number between zero and one (0<x<1) from a uniform distribution.

You can repeat a sequence of random numbers by storing a seed value in the random number generator. Seed values help you recreate experiments by generating the same series of random numbers.

To store a seed value, key in an integer greater than zero and press D & a.

Combinations & s

The calculator computes the number of combinations of n items taken r at a time. Both the n and r variables must be greater than or equal to 0.

-----------------------------

nr)! r!×–(

Permutations & m

The calculator computes the number of permutations of n items taken r at a time. Both the

n and r variables must be greater than or equal to 0.

------------------ nr)!–(

Rounding & o

The calculator computes using the rounded, displayed form of a number instead of the internally stored value.

10 Overview of Calculator Operations

For example, working in the Bond worksheet, you might want to round a computed selling price to the nearest penny (two decimal places) before continuing your calculation.

Note: The calculator stores values to an accuracy of up to 13 digits. The

decimal format setting rounds the displayed value but not the unrounded, internally stored value. (See “Choosing the Number of

Decimal Places Displayed” on page 4.)

Scientific Notation ;

When you compute a value in the standard-decimal format that is either too large or small to be displayed, the calculator displays it in scientific notation, that is, a base value (or mantissa), followed by a blank space, followed by an exponent.

With AOS™ selected, you can press ; to enter a number in scientific notation. (See “Choosing Calculation Methods

For example, to enter 3 Q 10

, key in 3 < 10 ; 3.

” on page 5.)

Overview of Calculator Operations 11

Memory Operations

You can store values in any of 10 memories using the standard calculator keys.

Note: You can also use the Memory worksheet. (See “Memory Worksheet

• You can store in memory any numeric value within the

range of the calculator.

• To access a memory M0 through M9, press a numeric

key (0 through 9).

Clearing Memory

Clearing memory before you begin a new calculation is a critical step in avoiding errors.

• To clear an individual memory, store a zero value in it.

• To clear all 10 calculator memories, press & { & z.

Storing to Memory

To store a displayed value to memory, press D and a numeric key (0–9).

• The displayed value replaces any previous value stored in the memory.

• The Constant Memory feature retains all stored values when you turn off the calculator.

” on page 80.)

Recalling From Memory

To recall a number stored in memory, press J and a numeric key (0–9).

Note: The recalled number remains in memory.

Memory Examples

To Pr es s

Clear memory 4 (by storing a zero value in it)

Store 14.95 in memory 3 (M3) 14.95 D 3

Recall a value from memory 7 (M7) J 7

0 D 4

Memory Arithmetic

Using memory arithmetic, you can perform a calculation with a stored value and store the result with a single operation.

12 Overview of Calculator Operations

• Memory arithmetic changes only the value in the affected memory and not the displayed value.

• Memory arithmetic does not complete any calculation in progress.

The table lists the available memory arithmetic functions. In each case, the specified memory stores the result.

To Pr es s

D H

Add the displayed value to the value stored in memory 9

M9).

(

Subtract the displayed value from the value stored in memory 3 (M3).

Multiply the value in memory 0 (M0) by the displayed value. D < 0

Divide the value in memory 5 (M5) by the displayed value. D 6 5

Raise the value in memory 4 (M4) to the power of the displayed value.

D B 3

D ; 4

Calculations Using Constants

To store a constant for use in repetitive calculations, enter a number and an operation, and then press &`.

To use the stored constant, key in a value and press N.

Note: Pressing a key other than a number or N clears the constant.

Example: Multiply 3, 7, and 45 by 8

To Press Display

Clear the calculator. & U 0.00

Enter the value for the first calculation.

Enter the operation and a constant value. <

Store the operation and value, and then calculate.

Calculate 7

Compute 45

Overview of Calculator Operations 13

Q 8.

8 8

& ` N 24.00

7 N 56.00

45 N 360.00

Keystrokes for Constant Calculations

This table shows how to create a constant for various operations.

To* Press**

Add c to each subsequent entry n H & ` c N Subtract c from each subsequent entry n B & ` c N Multiply each subsequent entry by cn < & ` c N Divide each subsequent entry by cn 6 & ` c N Raise each subsequent entry to the power of cn ; & ` c N Add c% of each subsequent entry to that entry n H & ` c 2 N Subtract c% of each subsequent entry from the

entry

*The letter c denotes the constant value. **Repeat constant calculations with n N.

n B & ` c 2 N

Last Answer Feature

Use the Last Answer ( repeatedly for the same value or to copy a value:

• From one place to another within the same worksheet

• From one worksheet to another

• From a worksheet to the standard-calculator mode

• From the standard-calculator mode to a worksheet

To display the last answer computed, press &x.

Note: The calculator changes the value of the last answer whenever it calculates a value automatically or whenever you:

• Press ! to enter a value.

• Press % to compute a value.

• Press N to complete a calculation.

ANS) feature with problems that call

Example: Using the Last Answer in a Calculation

To Press Display

Key in and complete a calculation 3 H 1 N 4.00

14 Overview of Calculator Operations

To Press Display

Key in a new calculation 2 ; 2.00

Recall the last answer & x 4.00

Complete the calculation N 16.00

Using Worksheets: Tools for Financial Solutions

The calculator contains worksheets with embedded formulas to solve specific problems. You apply settings or assign known values to worksheet variables and then compute the unknown value. Changing the values lets you ask what if questions and compare results.

Except for TVM variables, accessed in the standardcalculator mode, all variables are prompted.

For example, to assign values to amortization variables, you must first press & \ to access the Amortization worksheet.

Each worksheet is independent of the others: operations in a worksheet do not affect variables in other worksheets. When you exit a worksheet or turn off the calculator, the calculator retains all worksheet data.

To select Function Press

TVM worksheet (Chapter 2)

Amortization worksheet (Chapter 2)

Cash Flow worksheet (Chapter 3)

Bond worksheet (Chapter 4)

Depreciation worksheet (Chapter 5)

Overview of Calculator Operations 15

Analyzes equal cash flows, for example, annuities, loans, mortgages, leases, and savings

Performs amortization calculations and generates an amortization schedule

Analyzes unequal cash flows by calculating net present value and internal rate of return

Computes bond price and yield to maturity or call

Generates a depreciation schedule using one of six depreciation methods

,, -, ., /, 0, or & [

& \

& '

& l

& p

To select Function Press

Statistics worksheet (Chapter 6)

Analyzes statistics on one- or two-variable data using four

& k

regression analysis options

Percent Change/Compound Interest worksheet

Computes percent change, compound interest, and costsell markup

& q

(Chapter 7)

Interest Conversion worksheet (Chapter 7)

Converts interest rates between nominal rate (or annual percentage rate) and annual effective rate

Date worksheet (Chapter 7)

Computes number of days between two dates, or date/day of the week a specified number of days is from a given date

Profit Margin worksheet (Chapter 7)

Breakeven worksheet (Chapter 7)

Computes cost, selling price, and profit margin

Analyzes relationship between fixed cost, variable cost, price, profit, and quantity

Memory worksheet (Chapter 7)

Accesses storage area for up to 10 values

Accessing the TVM Worksheet Variables

• To assign values to the TVM worksheet variables, use the five TVM keys (,, -, ., /, 0).

• To access other TVM worksheet functions, press the & key, and then press a TVM function key (

BGN). (See “TVM and Amortization Worksheet

Variables” on page 22.)

Note: You can assign values to TVM variables while in a prompted worksheet, but you must return to the standard-calculator mode to calculate TVM values or clear the TVM worksheet.

& v

& u

& w

& r

& {

xP/Y, P/Y,

16 Overview of Calculator Operations

Accessing Prompted-Worksheet Variables

After you access a worksheet, press # or " to select variables. For example, press & \ to access the Amortization worksheet, and then press # or " to select the amortization variables (

).(See “TVM and Amortization Worksheet Variables” on page 22.)

INT

Indicators prompt you to select settings, enter values, or compute results. For example, the i# other variables. (See “Reading the Display” on page 2.)

To return to the standard-calculator mode, press & U.

$ indicators remind you to press # or " to select

P1, P2, BAL, PRN,

Types of Worksheet Variables

• Enter-only

• Compute-only

• Automatic-compute

• Enter-or-compute

•Settings

Note: The = sign displayed between the variable label and value indicates that the variable is assigned the value.

Enter-Only Variables

Values for enter-only variables must be entered, cannot be computed, and are often limited to a specified range, for example, value for an enter-only variable can be:

• Entered directly from the keyboard.

• The result of a math calculation.

• Recalled from memory.

• Obtained from another worksheet using the last answer feature.

When you access an enter-only variable, the calculator displays the variable label and ENTER indicator. The ENTER indicator reminds you to press ! after keying in a value to assign the value to the variable. After you press !, the  indicator confirms that the value is assigned.

P/Y and C/Y. The

Compute-Only Variables

You cannot enter values manually for compute-only variables, for example, net present value ( compute-only variable and press %. The calculator computes and displays the value based on the values of other variables.

Overview of Calculator Operations 17

NPV). To compute a value, display a

When you display a compute-only variable, the COMPUTE indicator reminds you to press % to compute its value. After you press %, the  indicator confirms that the displayed value has been computed.

Automatic-Compute Variables

When you press # or " to display an automatic-compute variable (for example, the Amortization worksheet computes and displays the value automatically without you having to press %.

INT variable), the calculator

Enter-or-Compute Variables in the TVM Worksheet

You can either enter or compute values for the TVM worksheet variables (N, I/Y, PV, PMT, and FV).

Note: Although you do not have to be in the standard-calculator mode to assign values to these variables, you must be in the standard-calculator mode to compute their values.

• To assign the value of a TVM variable, key in a number and press a variable key.

• To compute the value of a TVM variable, press %, and then press the variable key. The calculator computes and displays the value based on the values of other variables.

Enter-or-Compute Variables in Prompted Worksheets

You can either enter or compute values for some prompted worksheet variables (for example, the Bond worksheet YLD and PRI variables). When you select an enter-or-compute variable, the calculator displays the variable label with the

•The

•The COMPUTE indicator prompts you to press % to compute a

ENTER indicator prompts you to press ! to assign the keyed-

in value to the displayed variable.

value for the variable.

ENTER and COMPUTE indicators.

Selecting Worksheet Settings

Many prompted worksheets contain variables consisting of two or more options, or settings (for example, the Date worksheet ACT/360 variable). When you select variables with settings, the calculator displays the indicator and the current setting.

To scroll through the settings of a variable, press & V once for each setting.

18 Overview of Calculator Operations

SET

Display Indicators

•The  indicator confirms that the calculator entered the displayed value in the worksheet.

•The  indicator confirms that the calculator computed the displayed value.

• When a change to the worksheet invalidates either entered or computed values, the  and  indicators disappear.

Overview of Calculator Operations 19

20 Overview of Calculator Operations

Time-Value-of-Money and Amortization Worksheets

Use the Time-Value-of-Money (TVM) variables to solve problems with equal and regular cash flows that are either all inflows or all outflows (for example, annuities, loans, mortgages, leases, and savings).

For cash-flow problems with unequal cash flows, use the Cash Flow worksheet. (See “Cash Flow Worksheet page 41.)

After solving a TVM problem, you can use the Amortization worksheet to generate an amortization schedule.

• To access a TVM variable, press a TVM key (,, -, ., /, or 0).

• To access the prompted Amortization worksheet, press & \.

” on

Time-Value-of-Money and Amortization Worksheets 21

TVM and Amortization Worksheet Variables

Variable Key Display Type of Variable

Number of periods ,

Interest rate per year -

Present value .

Payment /

Future value 0

Number of payments per year & [

Number of compounding

periods per year

End-of-period payments & ]

Beginning-of-period

& V

payments

Starting payment & \

Ending payment #

Balance #

Principal paid #

Interest paid #

I/Y

PMT

P/Y

C/Y

END

BGN

BAL

PRN

INT

Enter-or-compute

Enter-only

Setting

Enter-only

Auto-compute

Note: This guidebook categorizes calculator variables by the method of entry. (See “Types of Worksheet Variables” on page 17.)

Using the TVM and Amortization Variables

Because the calculator stores values assigned to the TVM variables until you clear or change them, you should not have to perform all steps each time you work a problem.

• To assign a value to a TVM variable, key in a number and press a TVM key (,, -, ., /, 0).

• To change the number of payments ( number, and press !. To change the compounding periods (C/Y), press &[ #, key in a number, and press !.

• To change the payment period (END/BGN), press & ], and then press & V.

• To compute a value for the unknown variable, press %, and then press the key for the unknown variable.

22 Time-Value-of-Money and Amortization Worksheets

P/Y), press &[, key in a

• To generate an amortization schedule, press & \, enter the first and last payment number in the range (

P1 and P2), and press "

or # to compute values for each variable (BAL, PRN, and INT).

Resetting the TVM and Amortization Worksheet Variables

• To reset all calculator variables and formats to default values (including TVM and amortization variables), press & } !:

Variable Default Variable Default

I/Y

PMT

P/Y

C/Y

END/BGN END

BAL

PRN

INT

• To reset only the TVM variables (

N, I/Y, PV, PMT, FV) to default values,

press & ^.

• To reset P/Y and C/Y to default values, press & [ & z.

• To reset the Amortization worksheet variables (P1, P2, BAL, PRN,

INT) to default values, press & z while in the Amortization

worksheet.

• To reset END/BGN to the default value, press & ] & z.

Clearing the Unused Variable

For problems using only four of the five TVM variables, enter a value of zero for the unused variable.

For example, to determine the present value (

PV) of a known future

value (FV) with a known interest rate (I/Y) and no payments, enter 0 and

PMT.

press

Entering Positive and Negative Values for Outflows and Inflows

Enter negative values for outflows (cash paid out) and positive values for inflows (cash received).

Note: To enter a negative value, press S after entering the number. To change a negative value to positive, press S.

Time-Value-of-Money and Amortization Worksheets 23

Entering Values for I/Y, P/Y, and C/Y

•Enter I/Y as the nominal interest rate. The TVM worksheet automatically converts

P/Y and C/Y.

I/Y to a per period rate based on the values of

• Entering a value for P/Y automatically enters the same value for C/Y. (You can change C/Y.)

Specifying Payments Due With Annuities

Use END/BGN to specify whether the transaction is an ordinary annuity or an annuity due.

•Set

END for ordinary annuities, in which payments occur at the end

of each payment period. (This category includes most loans.)

•Set BGN for annuities due, in which payments occur at the beginning of each payment period. (This category includes most leases.)

Note: When you select beginning-of-period payments, the BGN indicator appears. (No indicator appears for END payments.)

Updating P1 and P2

To update P1 and P2 for a next range of payments, press % with P1 or

P2 displayed.

Different Values for BAL and FV

The computed value for BAL following a specified number of payments might be different than the computed value for FV following the same number of payments.

• When solving for

BAL, PRN, and INT, the calculator uses the PMT

value rounded to the number of decimal places specified by the decimal format.

• When solving for FV, the calculator uses the unrounded value for

PMT.

Entering, Recalling, and Computing TVM Values

• To enter a TVM value, key in the value and store it by pressing a TVM key (,, -, ., /, 0).

• To display a stored TVM value, press J and a TVM key.

You can enter or recall a value for any of the five TVM variables (

PV, PMT, or FV) in either the standard calculator mode or a worksheet

mode. The information displayed depends on which mode is selected.

• In standard calculator mode, the calculator displays the variable label, the = sign, and the value entered or recalled.

24 Time-Value-of-Money and Amortization Worksheets

N, I/Y,

• In worksheet modes the calculator displays only the value you enter or recall, although any variable label previously displayed remains displayed.

Note: You can tell that the displayed value is not assigned to the displayed variable, because the = indicator is not displayed.

To compute a TVM value, press % and a TVM key in standard-calculator mode.

Using [xP/Y] to Calculate a Value for N

1. Key in the number of years, and then press & Z to multiply by the stored

2. To assign the displayed value to

P/Y value. The total number of payments appears.

N for a TVM calculation, press ,.

Entering Cash Inflows and Outflows

The calculator treats cash received (inflows) as a positive value and cash invested (outflows) as a negative value.

• You must enter cash inflows as positive values and cash outflows as negative values.

• The calculator displays computed inflows as positive values and computed outflows as negative values.

Generating an Amortization Schedule

The Amortization worksheet uses TVM values to compute an amortization schedule either manually or automatically.

Generating an Amortization Schedule Manually

1. Press & \. The current P1 value appears.

2. To specify the first in a range of payments, key in a value for P1 and press !.

3. Press #. The current P2 value appears.

4. To specify the last payment in the range, key in a value for P2 and press !.

5. Press # to display each of the automatically computed values:

•

BAL— the remaining balance after payment P2

• PRN— the principal

• INT— the interest paid over the specified range

Time-Value-of-Money and Amortization Worksheets 25

6. Press & \. — or —

INT is displayed, press # to display P1 again.

7. To generate the amortization schedule, repeat steps 2 through 5 for each range of payments.

Generating an Amortization Schedule Automatically

After entering the initial values for P1 and P2, you can compute an amortization schedule automatically.

1. Press & \. — or —

INT is displayed, press # to display the current P1 value.

2. Press %. Both next range of payments.

The calculator computes the next range of payments using the same number of periods used with the previous range of payments. For example, if the previous range was 1 through 12 (12 payments), pressing % updates the range to 13 through 24 (12 payments).

3. Press # to display

• If you press % with P1 displayed, a new value for P2 will be

displayed automatically. (You can still enter a new value for P2.)

• If you did not press % with P1 displayed, you can press %

with P2 displayed to enter values for both P1 and P2 in the next range of payments.

4. Press # to display each of the automatically computed values for

BAL, PRN, and INT in the next range of payments.

5. Repeat steps 1 through 4 until the schedule is complete.

P1 and P2 update automatically to represent the

P2.

Example: Computing Basic Loan Interest

If you make a monthly payment of $425.84 on a 30-year mortgage for $75,000, what is the interest rate on your mortgage?

To Press Display

Set payments per year to 12. & [

Return to standard-calculator

& U

12 !

mode.

Enter number of payments

30 & Z ,

using the payment multiplier.

26 Time-Value-of-Money and Amortization Worksheets

P/Y=

12.00

0.00

360.00



To Press Display

Enter loan amount. 75000 .

Enter payment amount.

425.84 S /

Compute interest rate. % -

PV=

PMT=

I/Y=

75,000.00

-425.84

5.50

Answer: The interest rate is 5.5% per year.

Examples: Computing Basic Loan Payments

These examples show you how to compute basic loan payments on a $75,000 mortgage at 5.5% for 30 years.

Note: After you complete the first example, you should not have to reenter the values for loan amount and interest rate. The calculator saves the values you enter for later use.

Computing Monthly Payments

To Press Display

Set payments per year to 12. & [

Return to standard-calculator

& U

mode.

Enter number of payments

30 & Z ,

using payment multiplier.

Enter interest rate.

Enter loan amount.

5.5 -

75000 .

Compute payment. % /

12 !

P/Y=

I/Y=

PV=

PMT=

12.00

0.00

360.00

5.50

75,000.00

-425.84

õ







õ



Answer: The monthly payments are $425.84.

Computing Quarterly Payments

Note: The calculator automatically sets the number of compounding

periods (C/Y) to equal the number of payment periods (P/Y).

To Press Display

Set payments per year to 4. & [ 4 !

Return to standard-calculator

& U

mode.

Enter number of payments

30 & Z ,

using payment multiplier.

Time-Value-of-Money and Amortization Worksheets 27

P/Y=

4.00

0.00

120.00



To Press Display

Compute payment. % /

PMT=

-1,279.82



Answer: The quarterly payments are $1,279.82.

Examples: Computing Value in Savings

These examples show you how to compute the future and present values of a savings account paying 0.5% compounded at the end of each year with a 20-year time frame.

Computing Future Value

Example: If you open the account with $5,000, how much will you have

after 20 years?

To Press Display

Set all variables to defaults. & }

Enter number of payments. 20 ,

Enter interest rate.

Enter beginning balance.

.5 -

5000 S .

Compute future value. % 0

Answer: The account will be worth $5,524.48 after 20 years.

RST 0.00

I/Y=

PV=

FV=

20.00

0.50

-5,000.00

5,524.48





Computing Present Value

Example: How much money must you deposit to have $10,000 in 20

years?

To Press Display

Enter final balance.

10000 0

Compute present value. % .

FV=

PV=

10,000.00

-9,050.63





Answer: You must deposit $9,050.63.

28 Time-Value-of-Money and Amortization Worksheets

Example: Computing Present Value in Annuities

The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years. Assuming an annual discount rate of 10%, what is the present value of the savings using an ordinary annuity and an annuity due?

Cost Savings for a Present-Value Ordinary Annuity

Cost Savings for a Present-Value Annuity Due in a Leasing Agreement

To Press Display

Set all variables to defaults. & } !

Enter number of payments. 10 ,

Enter interest rate per

10 -

RST

I/Y=

0.00

10.00



payment period.

Enter payment.

Time-Value-of-Money and Amortization Worksheets 29

20000 S /

PMT=

-20,000.00



To Press Display

Compute present value

% .

PV=

122,891.34

(ordinary annuity).

Set beginning-of-period

& ] & V

BGN

payments.

Return to calculator mode. & U 0.00



Compute present value

% .

PV=

135,180.48



(annuity due).

Answer: The present value of the savings is $122,891.34 with an ordinary

annuity and $135,180.48 with an annuity due.

Example: Computing Perpetual Annuities

To replace bricks in their highway system, the Land of Oz has issued perpetual bonds paying $110 per $1000 bond. What price should you pay for the bonds to earn 15% annually?

To Press Display

Calculate the present value for a

110 6 15 2 N

perpetual ordinary annuity.

Calculate the present value for a

H 110 N

perpetual annuity due.

Answer: You should pay $733.33 for a perpetual ordinary annuity and

$843.33 for a perpetual annuity due.

A perpetual annuity can be an ordinary annuity or an annuity due consisting of equal payments continuing indefinitely (for example, a preferred stock yielding a constant dollar dividend).

Perpetual ordinary annuity

733.33

843.33

30 Time-Value-of-Money and Amortization Worksheets

Perpetual annuity due

Because the term (1 + I/Y / 100)-N in the present value annuity equations approaches zero as N increases, you can use these equations to solve for the present value of a perpetual annuity:

• Perpetual ordinary annuity

PMT

• Perpetual annuity due

--------------------------- -

I/Y()100÷

PV PMT

PMT

----------------------------

I/Y()100)⁄

Example: Computing Present Value of Variable Cash Flows

The ABC Company purchased a machine that will save these end-of-year amounts:

Year

Amount

Time-Value-of-Money and Amortization Worksheets 31

1234 $5000 $7000 $8000 $10000

Given a 10% discount rate, does the present value of the cash flows exceed the original cost of $23,000?

To Press Display

Set all variables to defaults. & }

Enter interest rate per cash flow

10 -

period.

Enter 1st cash flow.

Enter 1st cash flow period.

Compute present value of 1st cash

5000 S 0

1 ,

% .

flow.

Store in

M1. D 1

Enter 2nd cash flow. 7000 S 0

Enter 2nd cash flow period.

Compute present value of 2nd

2 ,

% .

cash flow.

Sum to memory. D H

Enter 3rd cash flow. 8000 S 0

Enter period number.

Compute present value of 3rd

3 ,

% .

cash flow.

Sum to memory. D H 1

Enter 4th cash flow. 10000 S 0

Enter period number.

4 ,

RST 0.00

I/Y=

FV=

PV=

FV=

PV=

FV=

PV= 6,010.52

FV=

10.00

-5,000.00

1.00

4,545.45

-7,000.00

2.00

5,785.12

-8,000.00

3.00

6,010.52

-10,000.00

4.00











32 Time-Value-of-Money and Amortization Worksheets

To Press Display

Compute present value of 4th cash flow.

Sum to memory. D H

Recall total present value. J 1

Subtract original cost. B 23000 N 171.23

Answer: The present value of the cash flows is $23,171.23, which exceeds

the machine’s cost by $171.23. This is a profitable investment.

Note: Although variable cash flow payments are not equal (unlike annuity payments), you can solve for the present value by treating the cash flows as a series of compound interest payments.

The present value of variable cash flows is the value of cash flows occurring at the end of each payment period discounted back to the beginning of the first cash flow period (time zero).

% .

PV=

6,830.13

23,171.23



Example: Computing Present Value of a Lease With Residual Value

The Peach Bright Company wants to purchase a machine currently leased from your company. You offer to sell it for the present value of the lease discounted at an annual interest rate of 22% compounded monthly. The machine has a residual value of $6500 with 46 monthly payments of $1200 remaining on the lease. If the payments are due at the beginning of each month, how much should you charge for the machine?

Time-Value-of-Money and Amortization Worksheets 33

The total value of the machine is the present value of the residual value plus the present value of the lease payments.

To Press Display

Set all variables to defaults. & } !

Set beginning-of-period

& ] & V

RST 0.00

BGN

payments.

Return to standard-calculator

& U 0.00

mode.

Enter number of payments.

Calculate and enter periodic

46 ,

22 6 12 N -

I/Y=

46.00

1.83



interest rate.

Enter residual value of asset.

6500 S 0

Compute residual present value. % .

Enter lease payment amount.

Compute present value of lease

1200 S /

% .

FV=

PV=

PMT=

PV=

-6,500.00

2,818.22

-1,200.00

40,573.18



payments.

Answer: Peach Bright should pay your company $40,573.18 for the

machine.

Example: Computing Other Monthly Payments

If you finance the purchase of a new desk and chair for $525 at 20% APR compounded monthly for two years, how much is the monthly payment?



To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [ 12 !

34 Time-Value-of-Money and Amortization Worksheets

RST 0.00

P/Y=

12.00



To Press Display

Return to standard-calculator

& U

0.00

mode

Enter number of payments using

2 & Z ,

24.00



payment multiplier.

Enter interest rate.

Enter loan amount.

20 -

525 .

Compute payment. % /

Answer: Your monthly payment is $26.72.

I/Y=

PV=

PMT=

20.00

525.00

-26.72





Example: Saving With Monthly Deposits

Note: Accounts with payments made at the beginning of the period are referred to as annuity due accounts. Interest begins accumulating earlier and produces slightly higher yields.

You invest $200 at the beginning of each month in a retirement plan. What will the account balance be at the end of 20 years, if the fund earns an annual interest of 7.5 % compounded monthly, assuming beginningof-period payments?

To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [ 12 !

Set beginning-of-period

& ] & V

RST 0.00

P/Y=

BGN

12.00



payments.

Return to standard-calculator

& U

0.00

mode.

Time-Value-of-Money and Amortization Worksheets 35

To Press Display

Enter number of payments

20 & Z ,

240.00



using payment multiplier.

Enter interest rate.

Enter amount of payment.

7.5 -

200 S /

Compute future value. % 0

I/Y=

PMT=

FV=

7.50

-200.00

111,438.31





Answer: Depositing $200 at the beginning of each month for 20 years

results in a future amount of $111,438.31.

Example: Computing Amount to Borrow and Down Payment

You consider buying a car for $15,100. The finance company charges

7.5% APR compounded monthly on a 48-month loan. If you can afford a

monthly payment of $325, how much can you borrow? How much do you need for a down payment?

To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [ 12

RST

P/Y=

0.00

12.00



Return to standard-calculator

& U

0.00

mode

Enter number of payments using

4 & Z ,

48.00



payment multiplier.

Enter interest rate.

Enter payment.

36 Time-Value-of-Money and Amortization Worksheets

7.5 -

325 S /

I/Y=

PMT=

-325.00

7.50



To Press Display

Compute loan amount. % .

Compute down payment H

15,100 S N

PV=

13,441.47

-1,658.53



Answer: You can borrow $13,441.47 with a down payment of $1,658.53.

Example: Computing Regular Deposits for a Specified Future Amount

You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account.

How much should you deposit if the annual interest rate is 0.5% with quarterly compounding?

Because C/Y (compounding periods per year) is automatically set

Note:

to equal P/Y (payments per year), you must change the C/Y value.

To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [ 12 !

Set compounding periods to 4. #

Set beginning-of-period

4 !

& ] & V

RST 0.00

P/Y=

C/Y=

BGN

12.00

4.00



payments.

Return to standard-calculator

& U

0.00

mode.

Enter number of deposits using

10 & Z ,

120.00



payment multiplier.

Enter interest rate.

Enter future value.

.5 -

25,000 0

Compute deposit amount. % /

I/Y=

FV=

PMT=

0.50

25,000.00

-203.13





Answer: You must make monthly deposits of $203.13.

Time-Value-of-Money and Amortization Worksheets 37

Example: Computing Payments and Generating an Amortization Schedule

This example shows you how to use the TVM and Amortization worksheets to calculate the monthly payments on a 30-year loan and generate an amortization schedule for the first three years of the loan.

Computing Mortgage Payments

Calculate the monthly payment with a loan amount of $120,000 and

6.125% APR.

To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [ 12 !

Return to standard-calculator

& U

mode.

Enter number of payments

30 & Z ,

using payment multiplier.

Enter interest rate.

Enter loan amount.

6.125 -

120000 .

Compute payment. % /

Answer: The computed monthly payment, or outflow, is $729.13.

RST 0.00

P/Y=

I/Y=

PV=

PMT=

12.00

0.00

360.00

6.13

120,000.00

-729.13



Generating an Amortization Schedule

Generate an amortization schedule for the first three years of the loan. If the first payment is in April, the first year has nine payment periods. (Following years have 12 payment periods each.)

To Press Display

Select the Amortization worksheet. & \

Set beginning period to 1. 1 !

Set ending period to 9. # 9 !

Display 1st year amortization data. #

# #

Change beginning period to 10. #

Change ending period to 21. #

38 Time-Value-of-Money and Amortization Worksheets

10 !

21 !

P1= 0

P1=

P2=

BAL= PRN= INT=

P1=

P2=

118,928.63

1.00

9.00

-1071.37*

-5,490.80*

10.00

21.00



To Press Display

Display 2nd year amortization data. #

# #

Move to

P1 and press % to enter

# %

BAL= PRN= INT=

P1=

117,421.60

_-1,507.03*

-7,242.53*

22.00

next range of payments.

Display

P2. #

Display 3rd year amortization data. #

# #

P2=

BAL= PRN= INT=

33.00

115,819.62

-1601.98*

-7,147.58*

Example: Computing Payment, Interest, and Loan Balance After a Specified Payment

A group of sellers considers financing the sale price of a property for $82,000 at 7% annual interest, amortized over a 30-year term with a balloon payment due after five years. They want to know:

• Amount of the monthly payment

• Amount of interest they will receive

• Remaining balance at the end of the term (balloon payment)

Computing the Monthly Payment



To Press Display

Set all variables to defaults. & } !

Set payments per year to 12. & [

Return to standard-calculator

& U 0.00

12 !

RST

P/Y=

0.00

12.00



mode.

Enter number of payments

30 & Z ,

360.00



using payment multiplier.

Enter interest rate.

Enter loan amount.

7 -

82000 .

Compute payment. % /

Time-Value-of-Money and Amortization Worksheets 39

I/Y=

PV=

PMT=

7.00

82,000.00

-545.55





Generating an Amortization Schedule for Interest and Balloon Payment

To Press Display

Select Amortization worksheet. & \

Enter end period (five years). #

View balance due after five

5 & Z !

years (balloon payment).

View interest paid after five

# #

years.

If the sellers financed the sale, they would receive:

• Monthly payment: $545.55 for five years

• Interest: $27,790.72 over the five years

• Balloon payment: $77,187.72

P1=

P2=

BAL=

INT=

60.00

77,187.72

-27,920.72

1.00





40 Time-Value-of-Money and Amortization Worksheets

Cash Flow Worksheet

Use the Cash Flow worksheet to solve problems with unequal cash flows.

To solve problems with equal cash flows, use the TVM worksheet. (See “Time-Value-of-Money and Amortization

Worksheets” on page 21.)

• To access the Cash Flow worksheet and initial cash flow value (

• To access the cash flow amount and frequency variables (Cnn/Fnn), press # or ".

• To access the discount rate variable (

CFo), press '.

I), press (.

• To compute net present value ( % for each variable.

• To compute the internal rate of return (

•

NPV), press # or " and

IRR), press ).

Cash Flow Worksheet Variables

Variable Key Display Variable

Type **

Initial cash flow '

Amount of nth cash flow

Frequency of nth cash flow

Discount rate (

Net present value # %

Internal rate of return )%

* nn represents the cash flow (C01–C24) or frequency (F01–F24)

number.

CFo

Cnn* Enter-only

Fnn* Enter-only

NPV

IRR

Enter-only

Compute-only

Cash Flow Worksheet 41

** This guidebook categorizes variables by the method of entry. (See

“Types of Worksheet Variables

” on page 17.)

Resetting Variables

• To reset CFo, Cnn, and Fnn to default values, press ' and then &z.

• To reset NPV to the default value, press ( and then &z.

• To reset IRR to the default value, press ) and then &z.

• To reset all calculator variables and formats to default values, including all Cash Flow worksheet variables, press &} !.

Entering Cash Flows

• You must enter an initial cash flow (CFo). The calculator accepts up to 24 additional cash flows (C01–C24). Each cash flow can have a unique value.

• Enter positive values for cash inflows (cash received) and negative values for cash outflows (cash paid out). To enter a negative value, key in a number and press S.

Inserting and Deleting Cash Flows

The calculator displays INS or DEL to confirm that you can press &X or & W to insert or delete cash flows.

Uneven and Grouped Cash Flows

Uneven Cash Flows

The Cash Flow worksheet analyzes unequal cash flows over equal time periods. Cash-flow values can include both inflows (cash received) and outflows (cash paid out).

All cash-flow problems start with an initial cash flow labeled always a known, entered value.

42 Cash Flow Worksheet

CFo. CFo is

Grouped Cash Flows

Cash-flow problems can contain cash flows with unique values as well as consecutive cash flows of equal value.

Although you must enter unequal cash flows separately, you can enter groups of consecutive, equal cash flows simultaneously using the variable.

Fnn

Entering Cash Flows

Cash flows consist of an initial cash flow (CFo) and up to 24 additional cash flows (C01-C24), each of which can have a unique value. You must enter the number of occurrences (up to 9,999), or frequency (F), for each additional cash flow (

• The calculator displays positive values for inflows (cash received) and negative values for outflows (cash paid out).

• To clear the Cash Flow worksheet, press & z.

To enter cash flows:

1. Press '. The initial cash-flow value (

2. Key in a value for CFo and press !.

3. To select an additional cash-flow variable, press #. The C01 value appears.

4. To change C01, key in a value and press !.

5. To select the cash-flow frequency variable ( value appears.

6. To change F01, key in a value and press !.

7. To select an additional cash-flow variable, press #. The C02 value appears.

8. Repeat steps 4 through 7 for all remaining cash flows and frequencies.

9. To review entries, press # or ".

C01-C24).

CFo) appears.

F01), press #. The F01

Deleting Cash Flows

When you delete a cash flow, the calculator decreases the number of subsequent cash flows automatically.

Cash Flow Worksheet 43

The DEL indicator confirms that you can delete a cash flow.

1. Press # or " until the cash flow you want to delete appears.

2. Press & W. The cash flow you specified and its frequency is deleted.

Inserting Cash Flows

When you insert a cash flow, the calculator increases the number of the following cash flows, up to the maximum of 24.

Note: The INS indicator confirms that you can insert a cash flow.

1. Press # or " to select the cash flow where you want to insert the new one. For example, to insert a new second cash flow, select

2. Press & X.

3. Key in the new cash flow and press !. The new cash flow is entered at

C02.

Computing Cash Flows

The calculator solves for these cash-flow values:

• Net present value ( including inflows (cash received) and outflows (cash paid out). A positive NPV value indicates a profitable investment.

44 Cash Flow Worksheet

NPV) is the total present value of all cash flows,

• Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows is equal to 0.

Computing NPV

1. Press ( to display the current discount rate (I).

2. Key in a value and press !.

3. Press # to display the current net present value (

NPV).

4. To compute the net present value for the series of cash flows entered, press %.

Computing IRR

1. Press ). The IRR variable and current value are displayed (based on the current cash-flow values).

2. To compute the internal rate of return, press %. The calculator displays the IRR value.

When solving for IRR, the calculator performs a series of complex, iterative calculations that can take seconds or even minutes to complete. The number of possible IRR solutions depends on the number of sign changes in your cash-flow sequence.

• When a sequence of cash flows has no sign changes, no exists. The calculator displays

Error 5.

IRR solution

• When a sequence of cash flows has only one sign change, only one

IRR solution exists, which the calculator displays.

• When a sequence of cash flows has two or more sign changes:

– At least one solution exists.

– As many solutions can exist as there are sign changes.

Cash Flow Worksheet 45

When more than one solution exists, the calculator displays the one closest to zero. Because the displayed solution has no financial meaning, you should use caution in making investment decisions based on an

IRR computed for a cash-flow stream with more than

one sign change.

The time line reflects a sequence of cash flows with three sign changes, indicating that one, two, or three

IRR solutions can exist.

• When solving complex cash-flow problems, the calculator might not

IRR, even if a solution exists. In this case, the calculator displays

find

Error 7 (iteration limit exceeded).

Example: Solving for Unequal Cash Flows

These examples show you how to enter and edit unequal cash-flow data to calculate:

• Net present value (

NPV)

• Internal rate of return (IRR)

A company pays $7,000 for a new machine, plans a 20% annual return on the investment, and expects these annual cash flows over the next six years:

Year Cash Flow Number Cash Flow Estimate

Purchase

2–5

CFo

C01

C02

C03

-$7,000

3,000

5,000 each year

4,000

As the time line shows, the cash flows are a combination of equal and unequal values. As an outflow, the initial cash flow (CFo) appears as a negative value.

46 Cash Flow Worksheet

Entering Cash-Flow Data

To Press Display

Select Cash Flow worksheet. '

Enter initial cash flow. 7000 S !

Enter cash flow for first year. #

3000 !

Enter cash flows for years two through five.

Enter cash flow for sixth year. #

5000 !

4 !

4000 !

CFo= 0.00

CFo=

C01= F01=

C02= F02=

C03= F03=

-7,000.00

3,000.00

1.00

5,000.00

4.00

4,000.00

1.00



Editing Cash-Flow Data

After entering the cash-flow data, you learn that the $4,000 cash-flow value should occur in the second year instead of the sixth. To edit, delete the $4,000 value for year 6 and insert it for year 2.

To Press Display

Move to third cash flow. "

Delete third cash flow. & W

Move to second cash flow. " "

Insert new second cash flow. & X

Move to next cash flow to verify data.

# #

4000 !

C03=

C03= 0.00

C02=

C02= F02=

C03= F03=

4,000.00

5,000.00

4,000.00

1.00

5,000.00

4.00



Cash Flow Worksheet 47

Computing NPV

Use an interest rate per period (I) of 20%.

To Press Display

Access interest rate variable (

Enter interest rate per period. 20 !

Compute net present value. # %

I= 0.00

NPV=

20.00

7,266.44





Answers:

NPV is $7,266.44.

Computing IRR

To Press Display

IRR. )

Access

Compute internal rate of return. # %

Answer: IRR is 52.71%.

IRR= 0.00

IRR=

52.71



Example: Value of a Lease with Uneven Payments

A lease with an uneven payment schedule usually accommodates seasonal or other anticipated fluctuations in the lessee’s cash position.

A 36-month lease has the following payment schedule and beginning-ofperiod payments.

Number of Months Payment Amount

4$0

8 $5000

3$0

9 $6000

2$0

10 $7000

If the required earnings rate is 10% per 12-month period with monthly compounding:

• What is the present value of these lease payments?

48 Cash Flow Worksheet

• What even payment amount at the beginning of each month would result in the same present value?

Because the cash flows are uneven, use the Cash Flow worksheet to determine the net present value of the lease.

Computing NPV

The cash flows for the first four months are stated as a group of four $0 cash flows. Because the lease specifies beginning-of-period payments, you must treat the first cash flow in this group as the initial investment

CFo) and enter the remaining three cash flows on the cash flow screens

( (C01 and F01).

Note: The BGN/END setting in the TVM worksheet does not affect the Cash Flow worksheet.

To Press Display

Set all variables to defaults. & } !

Select Cash Flow worksheet. '

Enter first group of cash flows. #

3 !

Enter second group of cash flows.

Enter third group of cash flows.

Enter fourth group of cash flows.

5000 S !

# # 8 !

# #

3 !

6000 S !

9 !

Enter fifth group of cash flows. #

2 !

Enter sixth group of cash flows. #

7000 S !

# 10 !

NPV. (

Select

Cash Flow Worksheet 49

RST

CFo= 0.00

C01= F01=

C02= F02=

C03= F03=

C04= F04=

C05= F05=

C06= F06=

I= 0.00

0.00

3.00

-5000.00

8.00

0.00

3.00

-6000.00

9.00

0.00

2.00

-7000.00

10.00



To Press Display

Enter monthly earnings rate. 10 6 12 !

Compute

NPV. # %

NPV=

0.83

-138,088.44





50 Cash Flow Worksheet

Bond Worksheet

The Bond worksheet lets you compute bond price, yield to maturity or call, and accrued interest.

You can also use the date functions to price bonds purchased on dates other than the coupon anniversary.

• To access the Bond worksheet, press & l.

• To access bond variables, press " or #.

• To change the options for day-count methods ( and 360) and coupons per year (2/Y and 1/Y), press & V once for each option.

Note: Pressing # or " to navigate through the Bond worksheet before

you enter values causes an error (Error 6). To clear the error, press P. (See “Error Messages

” on page 94.)

ACT

Bond Worksheet 51

Bond Worksheet Variables

Variable Key Display Variable Type

Settlement date & l

Annual coupon rate in percent #

Redemption date #

Redemption value (percentage of

SDT

CPN

RDT

par value)

Actual/actual day-count method #

30/360 day-count method & V

Two coupons per year #

One coupon per year & V

Yield to redemption #

Dollar price #

Accrued interest #

ACT

360

2/Y

1/Y

YLD

PRI

Resetting Bond Worksheet Variables

• To reset the Bond worksheet variables to default values, press & z while in the Bond worksheet.

Variable Default Variable Default

SDT

CPN

RDT

12-31-1990

100

ACT/360 ACT

2/Y, 1/Y 2/Y

YLD 0

PRI 0

Enter only

Setting

Enter/compute

Auto-compute

• To reset all calculator variables and formats to default values, including the Bond worksheet variables, press &}!.

Entering Dates

• Use the following convention to key in dates: mm.ddyy or dd.mmyy. After keying in the date, press !.

Note: You can display dates in either US or European format. (See “Setting Calculator Formats ” on page 4.)

• You can enter dates from January 1, 1950 through December 31,

2049.

52 Bond Worksheet

• The calculator assumes that the redemption date (RDT) coincides with a coupon date:

–To compute to maturity, enter the maturity date for RDT.

–To compute to call, enter the call date for RDT.

Entering CPN

CPN represents the annual coupon rate as a percentage of the bond par

value rather than the dollar amount of the coupon payment.

Entering RV

The redemption value (RV) is a percentage of the bond par value:

•For to maturity analysis, enter 100 for

•For to call analysis, enter the call price for RV.

RV.

Setting the Day-Count Method

1. To display the day-count method, press # until ACT or 360 appears.

2. To change the day-count method, press & V.

Setting the Coupon Frequency

1. To display the coupon frequency, press # until 1/Y or 2/Y appears.

2. To change the coupon frequency, press & V.

Bond Worksheet 53

Bond Worksheet Terminology

Term Definition

Call Date A callable bond can be retired by the issuing agency

before the maturity date. The call date for such a bond is printed in the bond contract.

Coupon Payment

Coupon Rate The annual interest rate printed on the bond.

Dollar Price Price of the security expressed in terms of dollars per

Par (Face) Value The value printed on the bond.

Premium Bond A bond that sells for an amount greater than the par

Discount Bond A bond selling for less than the par value.

Redemption Date

The periodic payment made to the owner of the bond as interest.

$100 of par value.

value.

The date on which the issuing agency retires the bond. This date can be the date of maturity or, for a callable bond, the call date.

Redemption Value

Settlement Date The date on which a bond is exchanged for funds.

Yield to Maturity

The amount paid to the owner of a bond when retired. If the bond is redeemed at the maturity date, the redemption value is the par value printed on the bond. If the bond is redeemed at a call date, the redemption value is the bond’s par value plus any call premium. The calculator treats the redemption value in terms of dollars per $100 of par value.

The rate of return earned from payments of principal and interest, with interest compounded semiannually at the stated yield rate. The yield to maturity takes into account the amount of premium or discount, if any, and the time value of the investment.

Entering Bond Data and Computing Results

To compute values for price (PRI) or yield (YLD) and accrued interest (AI), first enter the four known values for settlement date ( (CPN), redemption date (RDT), and redemption value (RV).

54 Bond Worksheet

SDT), coupon rate

If necessary, change the day-count method (ACT or 360) and couponfrequency ( until you clear the worksheet or change the values and settings.

Note: Dates are not changed when you clear a worksheet.

2/Y or 1/Y). The Bond worksheet stores all values and settings

Entering Known Bond Values

1. Press & l. The current SDT value appears.

2. To clear the worksheet, press & z.

3. If necessary, key in a new

4. Repeat step 3 for variable.

Note: To enter dates, use this convention: mm.ddyy (US) or dd.mmyy (European).

CPN, RDT, and RV, pressing # once for each

SDT value and press !.

Setting the Bond Day-Count Method and Coupon Frequency

1. To display the day-count method, press # until ACT or 360 appears.

2. To change the day-count method, press &V.

3. To display the coupon frequency, press # until

4. To change the coupon frequency, press & V.

2/Y or 1/Y appears.

Computing the Bond Price (PRI)

1. Press # until YLD appears.

2. Key in a value for YLD and press !.

3. Press # to display PRI, and then press %. The calculator displays the computed PRI value.

Computing the Bond Yield (YLD)

1. Press # until PRI appears.

2. Key in a value for PRI and press !.

3. Press # to display YLD, and then press %. The calculator displays the computed YLD value.

Computing Accrued Interest (AI)

To compute accrued interest, press # until the AI variable appears. The calculator automatically computes value.

Bond Worksheet 55

AI in terms of dollars per $100 of par

Example: Computing Bond Price and Accrued Interest

You consider buying a semiannual corporate bond maturing on December 31, 2007 and settling on June 12, 2006. The bond is based on the 30/360 day-count method with a coupon rate of 7%, redeemable at 100% of par value. For an 8% yield to maturity, compute the bond’s price and accrued interest, accrued interest, and modified duration.

Computing Bond Price and Accrued Interest

To Press Display

Select Bond worksheet. & l SDT =

Enter settlement date. 6.1206 ! SDT = 6-12-2006

12-31-1990

Enter coupon rate. #

Enter redemption date. #

Leave redemption value as is. # RV =

Select 30/360 day-count method.

Leave two coupon payments per year.

Enter yield. # 8 ! YLD = 8.00

Compute price # % PRI =

View modified duration # DUR =

Answer: The bond price is $98.56 per 100. The accrued interest is $3.15

per 100.

7 ! CPN = 7.00

12.3107 ! RDT = 12-31-2007

100.00

# & V 360

# 2/Y

98.56

1.44

56 Bond Worksheet

Depreciation Worksheet

The Depreciation worksheet lets you generate a depreciation schedule using your choice of depreciation methods.

• To access the Depreciation worksheet, press & p.

• To change depreciation methods, press &V until the desired method appears.

• To access other depreciation variables, press # or ". Note: To easily scroll up or down through a range of

variables, press and hold #

Depreciation Worksheet Variables

or ".

Variable Key Display

Straight-line method & p SL Setting

Sum-of-the-years’-digits method

Declining-balance method & V DB Setting/Enter

Declining-balance method with crossover to

French straight-line method* & V SLF Setting

French declining balance method*

Life of the asset in years # LIF Enter only

Starting month # M01 Enter only

Starting date for French straight-line method**

Cost of the asset # CST Enter only

Salvage value of the asset # SAL Enter only

Depreciation Worksheet 57

SL method

& V SYD Setting

& V DBX Setting/Enter

& V DBF Setting/Enter

# DT1 Enter only

Variab le Type

Variable Key Display

Year to compute # YR Enter only

Depreciation for the year # DEP Auto-compute

Variab le Type

Remaining book value at the end of the year

Remaining depreciable value # RDV Auto-compute

* SLF and DBF are available only if you select the European format for

dates or separators in numbers. (See “Setting Calculator Formats ” on page 4.)

** This guidebook categorizes variables by their method of entry. (See

“Types of Worksheet Variables

# RBV Auto-compute

” on page 17.)

Resetting the Depreciation Worksheet Variables

• To reset all calculator variables and formats to default values, including the Depreciation worksheet variables, press & } !.

Variable Default Variable Default

Depreciation method

DB 200 YR 1

DBX 200 CST 0

LIF 1 SAL 0

• To clear only the variables and reset default values without affecting the depreciation method or other calculator variables and formats, press & z while in the Depreciation worksheet.

SL M01 1

LIF, YR, CST, and SAL Depreciation worksheet

Computing Values for DEP, RBV, and RDV

• The calculator computes one year at a time and rounds the results to the number of decimal places set. (See “Setting Calculator Formats ” on page 4.)

• The calculator computes values for DEP, RBV, and RDV automatically when you press # to display each variable.

58 Depreciation Worksheet

Entering Values for DB and DBX

If you choose either the declining balance (DB) or declining balance with crossover to representing the percent of declining balance for the DB or DBX variable.

Note: The declining balance you enter must be a positive number.

SL (DBX) depreciation method, remember to enter a value

Entering Values for LIF

•If SL or SLF is selected, the LIF value must be a positive real number.

•If SYD, DB, DBX, or DBF is selected, the LIF value must be a positive integer.

Entering Values for M01

The value you enter for the starting month (M01) has two parts:

• The integer portion represents the month in which the asset is placed into service.

• The decimal portion represents the fraction of the initial month in which the asset begins to depreciate.

For example, to specify that the asset will begin to depreciate in the middle of the first month, enter 1.5. To specify that the asset will begin to depreciate a quarter of the way through the fourth month, enter 4.25.

Working with YR

• When computing depreciation, the value you enter for the year-tocompute (YR) variable must be a positive integer.

• If the remaining depreciable value (RDV) variable is displayed, you can press # to return to the year to compute (YR) variable. To represent the next depreciation year, press % to increment the value for

• To compute a depreciation schedule, repeatedly return to the year to compute (YR) variable, press % to increment the value for YR, and compute values for DEP, RBV, and RDV. The schedule is complete when

YR by one.

RDV equals zero.

Entering Data and Computing Results

Because the Depreciation worksheet stores values and settings until you either change them or clear the worksheet, you should not have to perform every step each time you work a problem.

Note: Dates are not changed when you clear a worksheet.

Depreciation Worksheet 59

Selecting a Depreciation Method

1. To access the Depreciation worksheet, press & p. The current depreciation method is displayed.

2. To clear the worksheet, press & z.

3. Press & V until you display the depreciation method you want (SL, SLF, SYD, DB, DBX, or DBF).

Note: If you select DB or DBX, you must either key in a value or accept the default of 200.

Entering Depreciation Data

1. To display LIF, press #.

2. Key in a value for

3. Repeat steps 1 and 2 for M01, DT1 (if SLF), CST, SAL, and YR.

Note: To select SLF or DBF, you must set either the European date or European separator format first. (See “Setting Calculator Formats ” on page 4.)

LIF and press !.

Computing Results for DEP, RBV, and RDV

After entering the data, press # once for each of the DEP, RBV, and RDV variables to display the computed values.

Note: The _indicator confirms that the displayed value is computed.

Generating a Depreciation Schedule

To generate a depreciation schedule and compute values for other years:

1. To display

2. To increment the value by one, press %.

3. To compute new values for DEP, RBV, and RDV, press # for each variable.

YR, press #.

60 Depreciation Worksheet

Example: Computing Straight-Line Depreciation

In mid-March, a company begins depreciation of a commercial building with a 31½ year life and no salvage value. The building cost $1,000,000. Use the straight-line depreciation method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years.

To Press Display

Access Depreciation

& p

worksheet.

Enter life in years. # 31.5 !

Enter starting month. #

Enter cost. #

3.5 !

1000000 !

Leave salvage value as is. #

Leave year as is. #

Display depreciation amount, remaining book value, and remaining

# # #

depreciable value.

View second year. #

Display second year depreciation data.

# # #

LIF =

M01 =

CST =

SAL = 0.00

YR = 1.00

DEP = RBV = RDV =

YR = YR =

DEP = RBV = RDV =

1,000,000.00

31.50

3.50

25,132.28*

974,867.72* 974,867.72*

1.00

2.00

31,746.03

943,121.69* 943,121.69*



Answer: For the first year, the depreciation amount is $25,132.28, the remaining book value is $974,867.72, and the remaining depreciable value is $974,867.72.

For the second year, the depreciation amount is $31,746.03, the remaining book value is $943,121.69, and the remaining depreciable value is $943,121.69.

Depreciation Worksheet 61

62 Depreciation Worksheet

Statistics Worksheet

The Statistics worksheet performs analysis on one-and two-variable data with four regression analysis models.

• To enter statistical data, press & j.

• To choose a statistics calculation method and compute the results, press &k.

• To access statistics variables, press # or ".

Statistics Worksheet Variables

Variable Key Display Variable Type

Current X value Current Y value

Standard linear regression Logarithmic regression Exponential regression Power regression One-variable statistics

Statistics Worksheet 63

& j#Xnn*

Ynn*

& k & V

LIN Ln EXP PWR 1-V

Enter-only Enter-only

Setting Setting Setting Setting Setting

Variable Key Display Variable Type

Number of observations Mean (average) of X values Sample standard deviation of X Population standard deviation of X Mean (average) of Y values Sample standard deviation of Y Population standard deviation of Y Linear regression y-intercept Linear regression slope Correlation coefficient Predicted X value Predicted Y value Sum of X values Sum of X squared values Sum of Y values Sum of Y squared values Sum of XY products

# (as needed)nv

sx y**

Sy** sy** a** b** r** X'** Y'**

GX GX

GY** GY

GXY**

Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute Enter/compute Enter/compute Auto-compute Auto-compute Auto-compute Auto-compute Auto-compute

* nn represents the number of the current X or Y value.

** Not displayed for one-variable statistics.

*** This guidebook categorizes calculator variables by their method of

entry. (See “Types of Worksheet Variables” on page 17.)

Resetting Statistics Worksheet Variables

•To clear all X and Y values as well as all values in the statistics portion of the worksheet without affecting the statistics calculation method, press & z while in the data-entry portion of the worksheet (& j).

• To reset the statistics calculation method to LIN and clear all values except and computation portion of the worksheet (&k).

• To reset the statistics calculation method to LIN and clear all values, including X and Y, press & } !.

X and Y, press &z while in the calculation method

Entering Data Points

• You can enter up to 50 (x,y) data points.

• If you press # or " to move through the portion of the worksheet that displays results without entering data points, the calculator will display an error.

64 Statistics Worksheet

• When you enter data for one-variable statistics, Xnn represents the value and

• When you enter a value for

Ynn specifies the number of occurrences (frequency).

Xnn, the value for Ynn defaults to 1.

Analyzing One-Variable Statistics

To analyze one-variable statistics, select 1-V. Only values for n, vvvv, Sx, sX, GX, and GX2 are computed and displayed for one-variable statistics.

Analyzing Two-Variable Statistics

You can choose from among these four regression-analysis methods:

•LIN

•

• EXP

• PWR

Computing Values Automatically

Except for the predicted X' and Y' values, the calculator computes and displays values for statistics variables automatically when you access them.

Using X' and Y' for Regression Predictions

To use the X' and Y' variables for regression predictions, you either can enter a value for

X' to compute Y' or enter a value for Y' to compute X'.

Regression Models

For two-variable data, the Statistics worksheet uses four regression models for curve fitting and forecasting.

Model Formula Restrictions

LIN

EXP

PWR

The calculator interprets the X value as the independent variable and the

Y value as the dependent variable.

The calculator computes the statistical results using these transformed values:

•

LIN uses X and Y.

Statistics Worksheet 65

Y = a + b X None

Y = a + b ln(X) All X values > zero

Y = a b

Y = a X

All Y values > zero

All X and Y values > zero

• Ln uses ln(X) and Y.

• EXP uses X and ln(Y).

• PWR uses ln(X) and ln(Y).

The calculator determines the values for curve that best fits the data.

a and b that create the line or

Correlation Coefficient

The calculator also determines r, the correlation coefficient, which measures the goodness of fit of the equation with the data. Generally:

•The closer

r is to 1 or -1, the better the fit.

r is to zero, the worse the fit.

Entering Statistical Data

Because the Statistics worksheet lets you enter and display up to 50 data points, and then stores the values until you clear the worksheet or change the values, you probably will not have to perform every step for each Statistics calculation.

1. To select the data-entry portion of the Statistics worksheet, press & j. X01 is displayed along with any previous value.

2. To clear the worksheet, press & z.

3. Key in a value for X01 and press !.

• For one-variable data, X01 is the first data point.

• For two-variable data, X01 is the first X value.

4. To display the Y01 variable, press #.

5. Key in a value for Y01 and press !.

• For one-variable data, you can enter the number of times the X

value occurs (frequency).

The default value is 1.

• For two-variable data, enter the first Y value.

6. To display the next X variable, press #.

7. Repeat steps 3 through 5 until you enter all of the data points.

Note: To easily scroll up or down through a range of variables, press and hold # or ".

66 Statistics Worksheet

Computing Statistical Results

Selecting a Statistics Calculation Method

1. Press & k to select the statistical calculation portion of the Statistics worksheet.

2. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V).

3. Press & V repeatedly until the statistics calculation method you want is displayed.

4. If you are analyzing one-variable data, select 1-V.

5. Press # to begin computing results.

Computing Results

To compute results based on the current data set, press # repeatedly after you have selected the statistics calculation method.

The calculator computes and displays the results of the statistical calculations (except for X' and Y') automatically when you access them.

For one-variable statistics, the calculator computes and displays only the

n, v

values for

Computing Y'

1. To select the Statistics worksheet, press & k.

2. Press " or # until X' is displayed.

3. Key in a value for X' and press !.

4. Press # to display the Y' variable.

5. Press % to compute a predicted Y' value.

v, Sx, sX, GX, and GX2.

Computing X'

1. To select the Statistics worksheet, press & k.

2. Press " or # until Y' is displayed.

3. Key in a value for Y' and press !.

4. Press " to display the X' variable.

5. Press % to compute an X' value.

Statistics Worksheet 67

68 Statistics Worksheet

Other Worksheets

The calculator also includes these worksheets:

• Percent Change/Compound Interest worksheet (&q)

• Interest Conversion worksheet (& v)

• Date worksheet (& u)

• Profit Margin worksheet (& w)

• Breakeven worksheet (& r)

• Memory worksheet (& {)

Percent Change/Compound Interest Worksheet

Use the Percent Change/Compound Interest worksheet to solve percent change, compound interest, and cost-sellmarkup problems.

• To access the Percent Change/Compound Interest worksheet, press &q.

• To access the Percent Change/Compound Interest variables, press # or ".

Percent Change/Compound Interest Worksheet Variables

Variable Key Display Variable Type

Old value/Cost &q

New value/Selling price #

Percent change/Percent markup

Number of periods #

Note: This guidebook categorizes variables by their method of entry. (See “Types of Worksheet Variables

Other Worksheets 69

OLD

NEW

%CH

#PD

” on page 17.)

Enter/compute

Resetting the Percent Change/Compound Interest Worksheet Variables

• To reset the Percent Change/Compound Interest variables to default values, press & z while in the Percent Change/Compound

Interest worksheet.

Variable Default Variable Default

OLD

NEW

%CH

#PD

• To reset default values for all calculator variables and formats, press & } !.

Entering Values

• For percent-change calculations, enter values for any two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown variable (leave represents a percentage increase; a negative percent change represents a percentage decrease.

• For compound-interest calculations, enter values for the three known variables and compute a value for the unknown fourth variable.

– OLD= present value

– NEW= future value

–

%CH= interest rate per period

– #PD= number of periods

• For cost-sell-markup calculations, enter values for two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown.

– OLD = cost

–

NEW= selling price

– %CH= percent markup

– #PD= 1

#PD=1). A positive percent change

Computing Values

1. To select the Percent Change/Compound Interest worksheet, press & q. The current value for OLD is displayed.

2. To clear the worksheet, press & z.

70 Other Worksheets

3. To enter values for the known variables, press # or " until the variable you want is displayed, then key in a value, and press !. (Do not enter a value for the variable you wish to solve.)

• Percent Change — Enter values for two of these three

variables:

OLD, NEW, and %CH. Leave #PD set to 1.

• Compound Interest — Enter values for three of these four

variables: OLD, NEW, %CH, and #PD.

• Cost-Sell-Markup — Enter values for two of these three

variables: OLD, NEW, and %CH. Leave #PD set to 1.

4. To compute a value for the unknown variable, press # or " until the variable you want is displayed and press %. The calculator displays the value.

Example: Computing Percent Change

First, determine the percentage change from a forecast amount of $658 to an actual amount of $700. Second, determine what the new amount would be if it were 7% below the original forecast.

To Press Display

Select Percent Change/Compound

& q

Interest worksheet.

Enter original forecast amount. 658 !

Enter actual amount. #

700 !

Compute percent change. # %

Enter -7 as percent change.

7 S !

Compute new actual amount. " %

OLD= 0

OLD=

NEW=

%CH=

NEW=

658.00

700.00

6.38

-7.00

611.94









Answer: $700 represents a 6.38% increase over the original forecast of

$658. A decrease of 7% would result in a new actual amount of $611.94.

Example: Computing Compound Interest

You purchased stock in 1995 for $500. Five years later, you sell the stock for $750. What was the annual growth rate?

To Press Display

Select Percent Change/Compound

& q

Interest worksheet.

Enter stock purchase price. 500 !

Enter stock selling price. #

Other Worksheets 71

750 !

OLD= 0

OLD=

NEW=

500.00

750.00



To Press Display

Enter number of years. # #

Compute annual growth rate. " %

Answer: The annual growth rate is 8.45%.

5 !

#PD=

%CH=

5.00

8.45

Example: Computing Cost-Sell-Markup

The original cost of an item is $100; the selling price is $125. Find the markup.

To Press Display

Select Percent Change/Compound Interest worksheet.

Clear worksheet variables. & z

Enter original cost. 100 !

& q

OLD= 0

OLD= 0.00

OLD=

100.00







Enter selling price. # 125 !

Compute percent markup. # %

Answer: The markup is 25%.

NEW=

%CH=

125.00

25.00





Interest Conversion Worksheet

The Interest Conversion worksheet converts interest rates between nominal rate (or annual percentage rate) and annual effective rate.

• To access the Interest Conversion worksheet, press & v.

• To select interest conversion variables, press # or ".

Variable Key Display Variable Type

Nominal rate & v NOM Enter/compute

Annual effective rate # EFF Enter/compute

Compounding periods per year # C/Y Enter-only

Note: The calculator categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 17.)

72 Other Worksheets

Comparing the Nominal Interest Rate of Investments

Comparing the nominal interest rate (annual percentage rate) of investments is misleading when the investments have the same nominal rate but different numbers of compounding periods per year.

To make a more valid comparison, convert the nominal interest rate

NOM) to the annual effective interest rate (EFF) for each investment.

(

• The nominal interest rate ( compounding period multiplied by the number of compounding periods per year.

• The annual effective interest rate (EFF) is the compound annual interest rate that you actually earn for the period of time stated.

NOM) is the interest rate per

Resetting Variables

• To reset all calculator variables and formats to default values, including the Interest Conversion worksheet variables, press & } !.

Variable Default

NOM 0

EFF 0

C/Y 1

• To clear the affecting worksheet.

NOM and EFF variables and reset default values without

C/Y, press & z in the Interest Conversion

Converting Variables

You can convert a nominal rate to an annual effective rate or vice versa.

Entering Values for Nom and EFF

Enter a value for NOM or EFF as an annual rate.

Converting Interest Rates

1. To access the Interest Conversion worksheet, press & v. The current NOM value appears.

2. To clear the worksheet, press & z.

3. Enter a value for the known interest rate (either NOM or EFF).

4. To enter a value for a known variable, press # or " until

EFF is displayed, key in a value, and press !.

5. Press # to display

Other Worksheets 73

C/Y. If necessary, change the value and press !.

NOM or

6. To compute a value for the unknown variable (interest rate), press # or " until

NOM or EFF is displayed, and then press %. The

calculator displays the computed value.

Example: A bank offers a certificate that pays a nominal interest rate of 15% with quarterly compounding. What is the annual effective interest rate?

To Press Display

Select Interest Conversion

& v NOM=

worksheet.

Enter nominal interest rate. 15 ! NOM= 15.00

Enter number of compounding

4 ! C/Y= 4.00

# #

periods per year.

Compute annual effective

" % EFF=

15.87

interest rate.

Answer: A nominal interest rate of 15% compounded quarterly is equivalent to an annual effective interest rate of 15.87%.

Date Worksheet

Use the Date worksheet to find the number of days between two dates. You can also compute a date and day of the week based on a starting date and a specified number of days.

• To access the Date worksheet, press & u.

• To access the date variables, press # or ".

• To select the day-count method ( & V once for each option.

ACT and 360), press

Date Worksheet Variables

Variable Key Display Variable Type

Date 1 & u DT1 Enter/compute

Date 2 # DT2 Enter/compute

Days between dates # DBD Enter/compute

Actual/actual day-count method #

30/360 day-count method #

74 Other Worksheets

ACT*Setting

360*Setting

Note: The calculator categorizes variables by their method of entry. (See

“Types of Worksheet Variables

” on page 17.)

Resetting the Date Worksheet Variables

• To reset default values for all calculator variables and formats, including the Date worksheet variables, press & } !.

Variable Default Variable Default

DT1 12-31-1990 DBD 0

DT2 12-31-1990 Day-count

method

• To clear Date worksheet variables and reset default values without affecting the day-count method, press &z while in the Date worksheet.

ACT

Entering Dates

• The calculator assumes that DT1 is earlier than DT2.

• Enter dates for DT1 and DT2 in the selected US or European date format.

• When you compute a date for DT1 or DT2, the calculator displays a three-letter abbreviation for the day of the week (for example,

WED).

Selecting the Day-Count Method Affects Calculations

• When you select ACT as the day-count method, the calculator uses the actual number of days in each month and each year, including adjustments for leap years.

• When you select 360 as the day-count method, the calculator assumes 30 days per month (360 days per year). You can compute

DBD using this day-count method, but not DT1 or DT2.

Computing Dates

1. To select the Date worksheet, press & u. The DT1 value is displayed.

2. To clear the worksheet, press & z.

3. Enter values for two of the three variables: DT1, DT2, and DBD.

Note: Do not enter a value for the variable you wish to solve for.

4. To enter a value for a variable, press # or " to display the variable.

5. Key in a value and press !.

Other Worksheets 75

6. To change the day-count method setting, press # until ACT or 360 is displayed.

7. To compute a value for the unknown variable, press # or " to display the variable, and then press %. The calculator displays the computed value.

Example: Computing Days between Dates

A loan made on September 4, 2003 defers the first payment until November 1, 2003. How many days does the loan accrue interest before the first payment?

To Press Display

Select Date worksheet. & u DT1=

Enter first date. 9.0403 ! DT1= 9-04-2003

12-31-1990

Enter second date. #

Select actual/actual day-count method.

Compute days between dates. " % DBD= 58.00

Answer: Because there are 58 days between the two dates, the loan accrues interest for 58 days before the first payment.

11.0103 ! DT2= 11-01-2003

# # ACT

Profit Margin Worksheet

The Profit Margin worksheet computes cost, selling price, and gross profit margin.

Note: To perform markup calculations, use the Percent Change/Compound Interest worksheet. (See “Percent

Change/Compound Interest Worksheet” on page 69.)

• To access the Profit Margin worksheet, press & w.

• To access profit margin variables, press " or #.

• Enter values for the two known variables, and then compute a value for the unknown variable.

Profit Margin Worksheet Variables

Variable Key Display Variable Type

Cost & w

CST

Enter/compute

76 Other Worksheets

Variable Key Display Variable Type

Selling price #

Profit margin #

Note: This guidebook categorizes calculator variables by their method of entry. (See “Types of Worksheet Variables

SEL

MAR

Enter/compute

” on page 17.)

Gross Profit Margin and Markup

The terms margin and markup often are used interchangeably, but each has a distinct meaning.

• Gross profit margin is the difference between selling price and cost, expressed as a percentage of the selling price.

• Markup is the difference between selling price and cost, expressed as a percentage of the cost.

Clearing Profit Margin Worksheet Variables

• To clear the Profit Margin worksheet variables and reset default values, press & z. All Profit Margin worksheet variables default to zero.

• To reset default values for all calculator variables and formats, including the Profit Margin worksheet variables, press & } !.

Computing Profit Margin

1. To select the Profit Margin worksheet, press & w. The CST value appears.

2. To enter a value for one of the two known variables, press # or " to select a variable, then key in a value and press !.

3. Repeat step 2 for the second known variable.

4. To compute a value for the unknown variable, press # or " to select the variable and press %. The calculator displays the computed value.

Example: Computing Profit Margin

The selling price of an item is $125. The gross profit margin is 20%. Find the original cost.

To Press Display

Select Profit Margin worksheet. &w

Enter selling price. # 125 !

Other Worksheets 77

CST= 0.00

SEL=

125.00



To Press Display

Enter profit margin. #

20 !

Compute cost. " " %

MAR=

CST=

20.00

100.00

Answer: The original cost is $100.

Breakeven Worksheet

The Breakeven worksheet computes the breakeven point and sales level needed to earn a given profit by analyzing relationships between fixed costs, variable costs per unit, quantity, price, and profit.

You operate at a loss until you reach the breakeven quantity (that is, total costs = total revenues).

• To access the Breakeven worksheet, press & r.

• To access breakeven variables, press " or #.

• Enter known values for the four known variables, then compute a value for the fifth, unknown variable.

Note: To solve for quantity (Q), enter a value of zero for profit (PFT).

Breakeven Worksheet Variables

Variable Key Display Variable Type

Fixed cost & r

Variable cost per unit #

Unit price #

Profit #

Quantity #

PFT

Enter/compute





Note: This guidebook categorizes calculator variables by their method of entry. (See “Types of Worksheet Variables” on page 17.)

Resetting the Breakeven Worksheet Variables

• To reset default values for all Breakeven worksheet variables, press & z. All Breakeven worksheet variables default to zero.

• To clear all calculator variables and formats and reset default values, including the Breakeven worksheet variables, press & } !.

78 Other Worksheets

Computing Breakeven

1. To access the Breakeven worksheet, press & r. The FC variable appears.

2. Press # or " to select a known variable, key in the value, and press !.

3. Repeat step 3 for each of the remaining known variables.

4. To compute a value for the unknown variable, press # or " until the variable is displayed, and then press %. The calculator displays the computed value.

Example: Computing Breakeven Quantity

A canoe company sells paddles for $20 each. The unit variable cost is $15, and the fixed costs are $3,000. How many paddles must be sold to break even?

To Press Display

Access Breakeven worksheet. & r

Enter fixed costs. 3000 !

Enter variable cost per unit. #

Enter price. #

15 !

20 !

Leave profit as is. #

Compute quantity. # %

FC= 0

FC=

VC=

PFT=

3,000.00

15.00

20.00

0.00

600.00





Answer: 600 paddles must be sold to break even.

Other Worksheets 79

Memory Worksheet

The Memory worksheet lets you compare and recall stored values by accessing the calculator’s 10 memories. All memory variables are enter-only. (See “Types of Worksheet

Variables” on page 17.)

• To access the Memory worksheet, press & {.

• To access memory variables, press " or #.

Note: You can access memories individually using D, J, and the digit keys. (See “Memory Operations

page 12.)

Memory Worksheet Variables

Variables Key Display Variable Type

Memory 0 & {

Memory 1 #

Memory 2 #

Memory 3 #

Memory 4 #

Memory 5 #

Memory 6 #

Memory 7 #

Memory 8 #

Memory 9 #

Enter-only

” on

Note: This guidebook categorizes calculator variables by their method of entry. (See “Types of Worksheet Variables” on page 17.)

Clearing the Memory Worksheet Variables

To clear all 10 memories at once, press & z in the Memory worksheet.

Using the Memory Worksheet

1. To select the Memory worksheet, press & {. M0 apears.

2. Perform any of the following operations:

• To clear all 10 memories at once, press & z.

80 Other Worksheets

• To view the contents of the memories, press # or " once for

each memory.

• To store a value, select a memory (M0-M9), key in a value, and

press !.

• Memory arithmetic. (See “Memory Arithmetic” on page 12.)

Examples: Using the Memory Worksheet

To Press Display

Access Memory worksheet & {

Select M4. # # # #

Clear M4. 0 !

Store 95.

Add 65. H

Subtract 30. B

Multiply by 95. <

Divide by 65. 6

Raise to 2

power.

9 5 !

6 5 !

3 0 !

9 5 !

6 5 !

;

2 !

M0= 0

M4= 0

M4=

12,350.00

36,100.00

0.00

95.00

160.00

130.00

190.00



Other Worksheets 81

82 Other Worksheets

Appendix — Reference Information

This appendix includes supplemental information to help you use your BA II PLUSé calculator:

•Formulas

• Error conditions

• Accuracy information

• IRR (internal-rate-of-return) calculations

• Algebraic operating system (AOS™)

• Battery information

• In case of difficulty

• TI product service and warranty information

Formulas

This section lists formulas used internally by the calculator.

Time Value of Money

where: PMT ƒÄ0

where:

The iteration used to compute

Appendix — Reference Information 83

yx1+()ln×()

[]1–=

y =C/Y P P/Y

=(.01 Q I/Y) P C/Y

=compounding periods per year

C/Y P/Y =payment periods per year I/Y =interest rate per year

–

FV PV÷()

PMT =0

1 N÷()

0 PV PMT G

1–=

11i+()

–

------------------------------

N–

×+×+=

FV 1 i+()

N–

I/Y =

100 CY e

yx1+()ln×()

1–[]×⁄×

where:

where: k =0 for end-of-period payments

where: i ƒ0

N = L(PV + FV) P PMT

where: i =0

PMT

where: i ƒ0

PMT = L(PV + FV) P N

where: i =0

x = i

=P/Y P C/Y

= 1 + i Q k

k =1 for beginning-of-period payments

PMT G

⎛⎞

----------------------------------------------

⎝⎠

PMT G

----------------------------------------------------------

–

-----

FV i×–×

PV i×+×

1 i+()ln

PV FV+

--------------------------- -

+×=

1 i+()

1–

PMT G

where: i ƒ0

PV = L(FV + PMT Q N)

where:

84 Appendix — Reference Information

------------------------

i =0

FV–

------------------ 1 i+()

PMT G

------------------------

–×=

⎨

⎧

PMT G

------------------------

where: i ƒ0

FV = L(PV + PMT Q N)

where:

i =0

– PV

1 i+()

×=

⎛⎞

⎝⎠

PMT G

------------------------

Amortization

If computing bal(), pmt2 = npmt Let bal(0) = RND(PV)

Iterate from

bal m() bal m 1–()I

⎩

then: bal( ) =bal(pmt2)

where:

Balance, principal, and interest are dependent on the values of

I/Y, and pmt1 and pmt2.

m = 1 to pmt2

RND RND12–i bal m 1–()×()[]=

– RND PMT() +=

GPrn( ) =bal(pmt2) N bal(pmt1) GInt( ) =(pmt2 N pmt1 +1) Q RND(PMT) N GPrn( )

RND =round the display to the number of decimal

places selected

RND12 =round to 12 decimal places

PMT, PV,

Cash Flow

NPV CF

where:

⎧ ⎪

⎨ ⎪ ⎩

CFj1 i+()

∑

j 1=

∑

i 1=

0 j 0=

j 1≥

Sj1–

11i+()

----------------------------------

–()

Appendix — Reference Information 85

Net present value depends on the values of the initial cash flow (CF

subsequent cash flows ( specified interest rate (i).

), frequency of each cash flow (n

), and the

IRR = 100 × i, where i satisfies npv() = 0

Internal rate of return depends on the values of the initial cash flow (CF0) and the subsequent cash flows (CF

i = I/Y ÷ 100

86 Appendix — Reference Information

PRI

100 R×

------------------

---------------------------------------

DSR

⎛

-----------

⎝

100 R×

---

------------------

×–=

⎞

---- -

⎠

Bonds

Price (given yield) with one coupon period or less to redemption:

where:

Note: The first term computes present value of the redemption amount, including interest, based on the yield for the invested period. The second term computes the accrued interest agreed to be paid to the seller.

Yield (given price) with one coupon period or less to redemption:

PRI =dollar price per $100 par value RV =redemption value of the security per $100 par value (RV =

100 except in those cases where call or put features must be considered)

R =annual interest rate (as a decimal; CPN _ 100) M =number of coupon periods per year standard for the

particular security involved (set to 1 or 2 in Bond worksheet)

DSR =number of days from settlement date to redemption date

(maturity date, call date, put date, etc.)

E =number of days in coupon period in which the settlement

date falls

Y =annual yield (as a decimal) on investment with security held

to redemption (YLD P 100)

A =number of days from beginning of coupon period to

settlement date (accrued days)

⎛⎞

-------- -

⎝⎠

100

---------------------------------------------------------------------------

PRI

⎛⎞

---- -

--------- -

–

⎝⎠

PRI

--------- 100

100

⎛⎞ ⎝⎠

⎛⎞

---

⎝⎠

---

---- -

×=

ME×

--------------

DSR

1. Source for bond formulas (except duration): Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association,

1986.

Appendix — Reference Information 87

Price (given yield) with more than one coupon period to redemption:

------------------------------------------ -

PRI

where: N =number of coupons payable between settlement date and

Note: The first term computes present value of the redemption amount, not including interest. The second term computes the present values for all future coupon payments. The third term computes the accrued interest agreed to be paid to the seller.

Yield (given price) with more than one coupon period to redemption:

Yield is found through an iterative search process using the “Price with more than one coupon period to redemption” formula.

Accrued interest for securities with standard coupons or interest at maturity:

⎛⎞ ⎝⎠

redemption date (maturity date, call date, put date, etc.). (If this number contains a fraction, raise it to the next whole number; for example, 2.4 = 3)

DSC =number of days from settlement date to next coupon date K =summation counter

DSC

----------- -

N 1–

---- -

---

××–

---- -

100

------------------------------------------ -

∑

K 1=

⎛⎞

⎝⎠

100

---- -

K 1–

---- -

DSC

----------- -

---- -

AI PAR

where:

AI =accrued interest PAR =par value (principal amount to be paid at maturity)

---

××=

Depreciation

RDV = CST N SAL N accumulated depreciation

Values for decimals you choose to be displayed.

In the following formulas,

88 Appendix — Reference Information

DEP, RDV, CST, and SAL are rounded to the number of

FSTYR = (13 N MO1) P 12.

Straight-line depreciation

CST SAL–

---------------------------

LIF

ST SAL–

First year:

--------------------------

LIF

FSTYR×

Last year or more:

DEP = RDV

Appendix — Reference Information 89

Sum-of-the-years’-digits depreciation

LIF 2 YR– FSTYR)–+ CST(× SAL )–

----------------------------------------------------------------------------------------------------

First year:

LIF(( LIF( 1))+× 2)÷

LIF CST SAL–()×

------------------------------------------------------------

LIF( LIF(× 1 )+()2)÷

FSTYR×

Last year or more:

DEP = RDV

Declining-balance depreciation

BV DB%×

------------------------------LIF 100×

where: RBV is for YR - 1

ST DB%×

First year:

Unless ; then use RDV Q FSTYR

DEP > RDV, use DEP = RDV

If computing last year, DEP = RDV

----------------------------- -

LIF 100×

ST DB%×

----------------------------- -

LIF 100×

FSTYR×

RDV>

Statistics

Note: Formulas apply to both x and y.

Standard deviation with n weighting (s

12⁄

⎛⎞

⎝⎠

∑

------------------- -

–

∑

---------------------------------------- -

90 Appendix — Reference Information

Standard deviation with n-1 weighting (s

x N

12⁄

⎛⎞

⎝⎠

∑

------------------- -

–

∑

---------------------------------------- -

Mean:

Regressions

Formulas apply to all regression models using transformed data.

n 1–

(

∑

---------------

( y

nxy)

∑

---------------------------------------------------------

() x

∑

---------------------------------

bδ

--------

Interest Rate Conversions

EFF 100 e

where: x =.01 Q NOM P CˆY

OM 100 CY⁄ e

where: x =.01 Q EFF

Percent Change

NEW OLD 1

()x

()–

∑

–

∑

–()

∑

()

∑

CY⁄ In× x 1÷()

( 1)–×=

1 CY In×⁄÷

(

%CH

⎛⎞

------------- -

⎝⎠

#PD

100

x 1+()

1)–××=

Appendix — Reference Information 91

where: OLD =old value

NEW =new value %CH =percent change #PD =number of periods

Profit Margin

Gross Profit Margin

Breakeven

PFT = P Q N (FC + VC Q)

Selling Price Cost–

----------------------------------------------Selling Price

100×=

where:

PFT =profit P =price FC =fixed cost VC =variable cost Q =quantity

Days between Dates

With the Date worksheet, you can enter or compute a date within the range January 1, 1950, through December 31, 2049.

Actual/actual day-count method

Note: The method assumes the actual number of days per month and

per year.

DBD (days between dates) = number of days II - number of days I Number of Days I

+ (number of days MB to M1) + DT1

Y1 YB–()

------------------------

Number of Days II=(Y2 - YB) Q 365

number of days MB to M2)

+ ( + DT2

= (Y1 - YB) Q 365

Y2 YB–()

------------------------

92 Appendix — Reference Information

where: M1 =month of first date

DT1 =day of first date Y1 =year of first date M2 =month of second date DT2 =day of second date Y2 =year of second date MB =base month (January) DB =base day (1) YB =base year (first year after leap year)

30/360 day-count method

Note: The method assumes 30 days per month and 360 days per year.

DBD Y2( Y1)–360× M2( M1 )++ 30× DT2( DT1)–+=

where:

Note: If change

M1 =month of first date DT1 =day of first date Y1 =year of first date M2 =month of second date DT2 =day of second date Y2 =year of second date

DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31,

DT2 to 30; otherwise, leave it at 31.

2. Source for 30/360 day-count method formula: Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association, 1986

Appendix — Reference Information 93

Error Messages

Note: To clear an error message, press P.

Error Possible Causes

Error 1

Overflow

Error 2

Invalid argument

• A result is outside the calculator range

(± 9.9999999999999E99).

• Tried to divide by zero (can occur internally).

• Tried to compute 1/x when x is zero.

• Statistics worksheet: a calculation included X or Y values that are all the same.

• Tried to compute x! when x is not an integer 0-69.

• Tried to compute LN of x when x is not > 0.

• Tried to compute yx when y < 0 and x is not an integer or the inverse of an integer.

Error 3

Too many pending operations

Error 4

Out of range

• Tried to compute when x < 0.

• Amortization worksheet: tried to compute

PRN, and INT when P2 < P1.

BAL,

• Depreciation worksheet: a calculation included

SAL > CST.

• More than 15 active levels of parentheses were tried in a calculation.

• A calculation tried to use more than 8 pending operations.

• Amortization worksheet: the value entered for

P2 is outside the range 1-9,999.

• TVM worksheet: the

• Cash Flow worksheet: the

P/Y or C/Y value  0.

Fnn value is outside the

range 0.5-9,999.

• Bond worksheet: the RV, CPN, or PRI value _0.

• Date worksheet: the computed date is outside the range January 1, 1950 through December 31, 2049.

• Depreciation worksheet: the value entered for: declining balance percent  0;

SAL < 0; or M01 1  M01  13.

• Interest Conversion worksheet: the

•The

DEC value is outside the range 0-9.

LIF  0; YR _ 0; CST <

C/Y value  0.

94 Appendix — Reference Information

Error Possible Causes

Error 5

No solution exists

• TVM worksheet: the calculator computed

FV, (N Q PMT), and PV all have the same sign.

(Make sure cash inflows are positive and outflows are negative.)

• TVM, Cash Flow, and Bond worksheets: the LN (logarithm) input is not > 0 during calculations.

• Cash Flow worksheet: the calculator computed without at least one sign change in the cash-flow list.

Error 6

Invalid date

• Bond and Date worksheets: a date is invalid (for example, January 32) or in the wrong format (for example, MM.DDYYYY instead of MM.DDYY.

• Bond worksheet: the calculator attempted a calculation with a redemption date earlier than or the same as the settlement date.

Error 7

Iteration limit exceeded

• TVM worksheet: the calculator computed very complex problem involving many iterations.

• Cash Flow worksheet: the calculator computed IRR for a complex problem with multiple sign changes.

• Bond worksheet: the calculator computed YLD for a very complex problem.

Error 8

Canceled iterative calculation

• TVM worksheet: $ was pressed to stop the evaluation of

• Amortization worksheet: $ was pressed to stop the evaluation of BAL or INT.

• Cash Flow worksheet: $ was pressed to stop the evaluation of

• Bond worksheet: $ was pressed to stop the evaluation of YLD.

• Depreciation worksheet: $ was pressed to stop the evaluation of DEP or RDV.

I/Y when

IRR

I/Y for a

I/Y.

IRR.

Accuracy Information

The calculator stores results internally as 13-digit numbers but displays them rounded to 10 digits or fewer, depending on the decimal format. The internal digits, or guard digits, increase the calculator’s accuracy. Additional calculations use the internal value, not the value displayed.

Appendix — Reference Information 95

Rounding

If a calculation produces a result with 11-digits or more, the calculator uses the internal guard digits to determine how to display the result. If the eleventh digit of the result is 5 or greater, the calculator rounds the result to the next larger value for display.

For example, consider this problem.

1 P 3 Q 3 = ?

Internally, the calculator solves the problem in two steps, as shown below.

1. 1 P 3 = 0.3333333333333

2. 0.3333333333333 Q 3 = 0.9999999999999

The calculator rounds the result and displays it as 1. This rounding enables the calculator to display the most accurate result.

Although most calculations are accurate to within ±1 in the last displayed digit, higher-order mathematical functions use iterative calculations, in which inaccuracies can accumulate in the guard digits. In most cases, the cumulative error from these calculations is maintained beyond the 10digit display so that no inaccuracy is shown.

AOS™ (Algebraic Operating System) Calculations

When you select the AOS calculation method, the calculator uses the standard rules of algebraic hierarchy to determine the order in which it performs operations.

Algebraic Hierarchy

The table shows the order in which the calculator performs operations using the AOS calculation method.

Priority Operations

1 (highest)

2 nCr, nPr

5 +, -

7 (lowest)

96 Appendix — Reference Information

, x!, 1/x, %, ‡x, LN, e2, HYP, INV, SIN, COS, TAN

Q, P

)

Texas Instruments BA II PLUS User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Important Information

USA FCC Information Concerning Radio Frequency Interference

Overview of Calculator Operations

Turning On the Calculator

Turning Off the Calculator

Selecting 2nd Functions

Reading the Display

Setting Calculator Formats

Resetting the Calculator

Clearing Calculator Entries and Memories

Correcting Entry Errors

Math Operations

Memory Operations

Calculations Using Constants

Last Answer Feature

Using Worksheets: Tools for Financial Solutions

Time-Value-of-Money and Amortization Worksheets

TVM and Amortization Worksheet Variables

Entering Cash Inflows and Outflows

Generating an Amortization Schedule

Example: Computing Basic Loan Interest

Examples: Computing Basic Loan Payments

Examples: Computing Value in Savings

Example: Computing Present Value in Annuities

Example: Computing Perpetual Annuities

Example: Computing Present Value of Variable Cash Flows

Example: Computing Present Value of a Lease With Residual Value

Example: Computing Other Monthly Payments

Example: Saving With Monthly Deposits

Example: Computing Amount to Borrow and Down Payment

Example: Computing Regular Deposits for a Specified Future Amount

Example: Computing Payments and Generating an Amortization Schedule

Example: Computing Payment, Interest, and Loan Balance After a Specified Payment

Cash Flow Worksheet

Cash Flow Worksheet Variables

Uneven and Grouped Cash Flows

Entering Cash Flows

Deleting Cash Flows

Inserting Cash Flows

Computing Cash Flows

Example: Solving for Unequal Cash Flows

Example: Value of a Lease with Uneven Payments

Bond Worksheet

Bond Worksheet Variables

Bond Worksheet Terminology

Entering Bond Data and Computing Results

Example: Computing Bond Price and Accrued Interest

Depreciation Worksheet

Depreciation Worksheet Variables

Entering Data and Computing Results

Example: Computing Straight-Line Depreciation

Statistics Worksheet

Statistics Worksheet Variables

Regression Models

Entering Statistical Data

Computing Statistical Results

Other Worksheets

Percent Change/Compound Interest Worksheet

Interest Conversion Worksheet

Date Worksheet

Profit Margin Worksheet

Breakeven Worksheet

Memory Worksheet

Formulas

Error Messages

Accuracy Information

AOS™ (Algebraic Operating System) Calculations