Texas Instruments BA II PLUS PROFESSIONAL User Manual | Manualsnet (2024)

BA II PLUS PROFESSIONAL

Calculator

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2011-2021 Texas Instruments Incorporated

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

2004-2019 Texas Instruments Incorporated

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Contents

Overview of Calculator Operations 1 TurningOn 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 andMemories 6 Correcting EntryErrors 7 Math Operations 8 MemoryOperations 12 CalculationsUsing Constants 14 Last Answer Feature 15 UsingWorksheets: Tools for FinancialSolutions 16

Time-Value-of-Money and Amortization Worksheets 21 TVM and AmortizationWorksheet Variables 21 Entering Cash InflowsandOutflows 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 PerpetualAnnuities 30 Example: Computing Present Value of Variable Cash Flows 31 Example: Computing Present Value of a LeaseWith ResidualValue 33 Example: Computing Other MonthlyPayments 34 Example: SavingWithMonthlyDeposits 35 Example: Computing Amount to Borrow and Down Payment 36 Example: Computing Regular Deposits for a Specified Future Amount 37 Example: Computing Payments andGenerating an Amortization Schedule 38 Example: Computing Payment, Interest, and Loan Balance After a Specified Pay-

ment 40

Cash Flow Worksheet 42 Cash FlowWorksheet Variables 42 Uneven andGrouped Cash Flows 44 Entering Cash Flows 44

Deleting Cash Flows 45 Inserting Cash Flows 45 Computing Cash Flows 46 Example: Solving for UnequalCash Flows 48 Example: Value of a Lease with Uneven Payments 51

Bond Worksheet 54 BondWorksheet Variables 54 BondWorksheet Terminology 56 Entering Bond Data and Computing Results 57 Example: Computing Bond Price, Accrued Interest, andModified Duration 58

Depreciation Worksheet 60 DepreciationWorksheet Variables 60 Entering Data and Computing Results 63 Example: Computing Straight-Line Depreciation 64

Statistics Worksheet 65 StatisticsWorksheet Variables 65 RegressionModels 67 Entering StatisticalData 68 Computing StatisticalResults 68

Other Worksheets 70 Percent Change/Compound InterestWorksheet 70 Interest ConversionWorksheet 74 DateWorksheet 76 Profit MarginWorksheet 78 BreakevenWorksheet 80 MemoryWorksheet 82

APPENDIX - Reference Information 84 Formulas 84 Error Messages 96 Accuracy Information 98 AOS (AlgebraicOperating System) Calculations 99 Battery Information 100 In Case of Difficulty 100

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General Information 102 Contact TI Support 102 Service andWarranty Information 102

Overview of Calculator Operations

This chapter describes the basic operation of your BA II PLUS PROFESSIONAL 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.

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

Overview of CalculatorOperations 1

2 Overview of CalculatorOperations

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 standard-calculator 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.)

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. (&

To cancel, press& again.

Indicator Meaning

INV Press a key to select its inverse trigonometric function.

HYP Press a key to select its hyperbolic function.

COMPUTE PressC to compute a value for the displayed variable.

ENTER Press! to assign the displayed value to the displayed variable.

SET Press&Vto 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".

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 BGN is not displayed, TVM calculations use end-of- period payments (END).

RAD Angle values appear in radians. When RAD is not displayed, angle values appear and must be entered in degrees.

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

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

= The displayed variable is assigned the displayed value.

The displayed value is negative.

Overview of CalculatorOperations 3

4 Overview of CalculatorOperations

Setting Calculator Formats

You can change these calculator formats:

To Select Press Display Default

Number of decimal places

&

|

DEC 09 (Press 9 for floating- decimal)

2

Angle units # DEG (degrees)

RAD (radians) DEG

Dates # US (mm-dd-yyyy)

Eur (dd-mm-yyyy) US

Number separators

# US (1,000.00 )

Eur (1.000,00) US

Calculation method

#

Chn (chain)

AOS (algebraic operating system)

Chn

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.

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.

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 3H 2< 4N, the Chn answer is 20 (3 + 2 = 5, 5 * 4 = 20).

Using AOS (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 3H 2< 4N, 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 CalculatorOperations 5

6 Overview of CalculatorOperations

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 section 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.)

Pressing 2nd Reset ENTER 1. Press&}. The RST ? and ENTER indicators appear.

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, pressP to clear the display before attempting to reset.

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 *

To clear Press

keyed in

An incorrect entry, error condition, or error message P

The prompted worksheet and reset default values &z

Calculator format settings and reset default values &|

&z

Out of the prompted worksheet and return to standard-calculator mode

All pending operations in standard-calculator mode

&U

In a prompted worksheet, the variable value keyed in but not entered (the previous value appears)

Any calculation started but not completed

PP

TVM worksheet variables and reset default values &U

&^

One of the 10 memories (without affecting the others)

QD and a memory number key (09)

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 or4).

To clear the last digit displayed, press*.

To clear the entire number displayed, pressP.

Note: PressingP 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.

Overview of CalculatorOperations 7

8 Overview of CalculatorOperations

To Press Display

Begin the expression 3 < 3.00

Enter a number 1234.86 1,234.86

Erase the entry error ** 1,234.

Key in the correct number 56 1,234.56

Compute the result N 3,703.68

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 pressN to complete.

To Press Display

Add 6 + 4 6 H 4 N 10.00

Subtract 6 N 4 6B 4 N 2.00

Multiply 6 Q 4 6 < 4 N 24.00

Divide 6 P 4 66 4 N 1.50

Find universal power: 31.25 3; 1.25 N 3.95

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

56.00

Find percent: 4% of $453 453 < 4 2N 18.12

Find percent ratio: 14 to 25 146 25 2N 56.00

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

498 H 7 2

N

34.86 532.86

Find price with percent discount: $69.99 N 10%

69.99B 10 2 N

7.00 62.99

To Press Display

Square 6.32 6.34 39.69

Find number of combinations where: n = 52, r = 5

52&s 5 N 2,598,960.00

Find number of permutations where: n = 8, r = 3

8&m 3 N 336.00

These operations do not require you to pressN to complete.

To Press Display

Find square root: 15.53 3.94

Find reciprocal: 1/3.2 3.25 0.31

Find factorial: 5! 5&g 120.00

Find natural logarithm: ln 203.45 203.45> 5.32

Find natural antilogarithm: e.69315 .69315&i 2.00

Round 2 P 3 to the set decimal format 26 3 N&o 0.67

Generate random number* &a 0.86

Store seed value D&a 0.86

Find sine:** sin(11.54) 11.54&d 0.20

Find cosine:** cos(120) 120&e -0.50

Find tangent:** tan(76) 76&f 4.01

Find arcsine:** sin-1(.2) .28d 11.54

Find arccosine:** cos-1(-.5) .5S8e 120.00

Find arctangent:** tan-1(4) 48f 75.96

Find hyperbolic sine: sinh(.5) .5&cd 0.52

Find hyperbolic cosine: cosh(.5) .5&ce 1.13

Find hyperbolic tangent: tanh(.5) .5&cf 0.46

Find hyperbolic arcsine: sinh-1(5) 5&c8d 2.31

Find hyperbolic arccosine: cosh-1(5) 5&c8e 2.29

Overview of CalculatorOperations 9

10 Overview of CalculatorOperations

To Press Display

Find hyperbolic arctangent: tanh-1(.5) .5&c8f 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).

Universal Power; Press; to raise the displayed postive number to any power (for example, 2-5

or 2(1/3).)

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.

Parentheses9: 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. PressingN 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<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 0.

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 0.

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

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.)

Overview of CalculatorOperations 11

12 Overview of CalculatorOperations

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 103, key in 3 < 10; 3.

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, pressD and a numeric key (09).

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.

Recalling FromMemory To recall a number stored in memory, pressJ and a numeric key (09).

Note: The recalled number remains in memory.

Memory Examples

To Press

Clear memory 4 (by storing a zero value in it) 0D 4

Store 14.95 in memory 3 (M3) 14.95D 3

Recall a value from memory 7 (M7) J 7

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

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 Press

Add the displayed value to the value stored in memory 9 (M9).

DH

9

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

DB

3

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

Divide the value in memory 5 (M5) by the displayed value. D6

5

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

D;

4

Overview of CalculatorOperations 13

14 Overview of CalculatorOperations

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 pressN.

Note: Pressing a key other than a number orN 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. 3 3

Enter the operation and a constant value. < 8 8

Store the operation and value, and then calculate.

&`

N 24.00

Calculate 7 Q 8. 7 N 56.00

Compute 45 Q 8. 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. nH&` cN

Subtract c from each subsequent entry. nB&` cN

Multiply each subsequent entry by c. n<&` cN

Divide each subsequent entry by c. n6&` cN

Raise each subsequent entry to the power of c. n;&` cN

Add c% of each subsequent entry to that entry. nH&` c2N

Subtract c% of each subsequent entry from the entry.

nB&` c2N

* The letter c denotes the constant value.

** Repeat constant calculations with nN.

Last Answer Feature

Use the Last Answer (ANS) feature with problems that call 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.

PressC to compute a value.

PressN to complete a calculation.

Example: Using the Last Answer in a Calculation

To Press Display

Key in and complete a calculation 3 H 1 N 4.00

Key in a new calculation 2; 2.00

Recall the last answer &x 4.00

Complete the calculation N 16.00

Overview of CalculatorOperations 15

16 Overview of CalculatorOperations

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 standard-calculator 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

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

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

Amortization worksheet Performs amortization calculations and generates an amortization schedule

&\

Cash Flow worksheet

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

&'

Bond worksheet Computes bond price and yield to maturity or call

&l

Depreciation worksheet Generates a depreciation schedule using one of six depreciation methods

&p

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

&k

To select Function Press

regression analysis options

Percent Change/Compound Interest worksheet

Computes percent change, compound interest, and cost- sell markup

&q

Interest Conversion worksheet

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

&v

Date worksheet

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

&u

Profit Margin worksheet Computes cost, selling price, and profit margin

&w

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

&r

Memory worksheet Accesses storage area for up to 10 values

&{

Accessing the TVMWorksheet 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 (xP/Y, P/Y, BGN). See: TVM and Amortization Worksheet Variables.

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.

Overview of CalculatorOperations 17

18 Overview of CalculatorOperations

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 (P1, P2, BAL, PRN, INT). See: TVM and Amortization Worksheet Variables.

Indicators prompt you to select settings, enter values, or compute results. For example, the# and" indicators remind you to press# or" to select other variables.

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

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, P/Y and C/Y. The 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 1 indicator confirms that the value is assigned.

Compute-Only Variables

You cannot enter values manually for compute-only variables, for example, net present value (NPV). To compute a value, display a compute-only variable and pressC. The calculator computes and displays the value based on the values of other variables.

When you display a compute-only variable, the COMPUTE indicator reminds you to pressC to compute its value. After you pressC, the 7 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 INT variable), the calculator computes and displays the value automatically without you having to pressC.

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, pressC, 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 ENTER and COMPUTE indicators.

The ENTER indicator prompts you to press! to assign the keyed-in value to the displayed variable.

The COMPUTE indicator prompts you to pressC to compute a value for the variable.

Overview of CalculatorOperations 19

20 Overview of CalculatorOperations

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 SET indicator and the current setting.

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

Display Indicators

The 1 indicator confirms that the calculator entered the displayed value in the worksheet.

The 7 indicator confirms that the calculator computed the displayed value.

When a change to the worksheet invalidates either entered or computed values, the 1 and 7 indicators disappear.

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.)

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 (,,-,.,/,or0).

To access the prompted Amortization worksheet, press&\.

TVM and Amortization Worksheet Variables

Variable Key Display Type of Variable

Number of periods , N Enter-or- compute

Interest rate per year - I/Y Enter-or- compute

Present value . PV Enter-or- compute

Payment / PMT Enter-or- compute

Future value 0 FV Enter-or- compute

Number of payments per year &[ P/Y Enter-only

Number of compounding periods per year

# C/Y Enter-only

Time-Value-of-Money and Amortization Worksheets 21

22 Time-Value-of-Money and Amortization Worksheets

Variable Key Display Type of Variable

End-of-period payments &] END Setting

Beginning-of-period payments

&V BGN Setting

Starting payment &

\ P1 Enter-only

Ending payment # P2 Enter-only

Balance # BAL Auto-compute

Principal paid # PRN Auto-compute

Interest paid # INT Auto-compute

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

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 (P/Y), press&[, key in a 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, pressC, and then press the key for the unknown variable.

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

N 0 END/BGN END

I/Y 0 P1 1

PV 0 P2 1

PMT 0 BAL 0

FV 0 PRN 0

P/Y 1 INT 0

C/Y 1

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 press PMT.

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, pressS after entering the number. To change a negative value to positive, pressS.

Entering Values for I/Y, P/Y, and C/Y Enter I/Y as the nominal interest rate. The TVM worksheet automatically

converts I/Y to a per period rate based on the values of P/Y and C/Y.

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

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24 Time-Value-of-Money and Amortization Worksheets

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, pressC 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, pressJ and a TVM key.

You can enter or recall a value for any of the five TVM variables (N, I/Y, 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.

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

2. To assign the displayed value to 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

6. Press&\. or If INT is displayed, press# to display P1 again.

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26 Time-Value-of-Money and Amortization Worksheets

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

2. PressC. Both P1 and P2 update automatically to represent the 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 C updates the range to 13 through 24 (12 payments).

3. Press# to display P2.

If you pressC 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 pressC with P1 displayed, you can pressC 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.

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 &[ 12! P/Y= 12.001

Return to standard-calculator mode

&U 0.00

Enter number of payments 30&Z, N= 360.001

To Press Display

using the payment multiplier

Enter loan amount 75000. PV= 75,000.00 1

Enter payment amount 425.84S/ PMT= -425.841

Compute interest rate C- I/Y= 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 re-enter 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 &[ 12! P/Y= 12.001

Return to standard-calculator mode

&U 0.00

Enter number of payments using payment multiplier

30&Z, N= 360.001

Enter interest rate 5.5- I/Y= 5.501

Enter loan amount 75000. PV= 75,000.001

Compute payment C/ PMT= -425.847

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).

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28 Time-Value-of-Money and Amortization Worksheets

To Press Display

Set payments per year to 4 &[4! P/Y= 4.001

Return to standard-calculator mode

&U 0.00

Enter number of payments using payment multiplier

30&Z, N= 120.001

Compute payment C/ PMT= -1,279.827

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 &}! RST 0.00

Enter number of payments 20 , N= 20.001

Enter interest rate .5- I/Y= 0.501

Enter beginning balance 5000S. PV= -5,000.001

Compute future value C0 FV= 5,524.487

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

Computing Present Value Example: How much money must you deposit to have $10,000 in 20 years?

To Press Display

Enter final balance 100000 FV= 10,000.001

Compute present value C. PV= -9,050.637

Answer: You must deposit $9,050.63.

Example: Computing Present Value in Annuities

The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years. Assuming an annual disc