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
To clear The prompted worksheet and reset default values Calculator format settings and reset default values Out of the prompted worksheet and return to standard-calculator mode All pending operations in standard-calculator mode In a prompted worksheet, the variable value keyed in but not entered (the previous value appears) Any calculation started but not completed
Press &z &| &z &U
TVM worksheet variables and reset default values One of the 10 memories (without affecting the others)
&U &^ Q D 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 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 Begin the expression. Enter a number. Erase the entry error. Key in the correct number. Compute the result.

3< 1234.86

Display
3.00 1,234.86 1,234. 1,234.56 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 press N to complete. To Add 6 + 4 Subtract 6 N 4 Multiply 6 Q 4 Divide 6 P 4 Find universal power: 3
6H4N 6B4N 6<4N 664N 3 ; 1.25 N 7 <H 5 :N 453 < N N 498 H 7 2
10.00 2.00 24.00 1.50 3.95 56.00 18.12 56.00 34.86 532.86 7.00 62.99 2,598,960.00 336.00
Use parentheses: 7 Q (3 + 5) Find percent: 4% of $453 Find percent ratio: 14 to 25 Find price with percent add-on: $498 + 7% sales tax Find price with percent discount: $69.99 N 10% Find number of combinations where: n = 52, r = 5

69.99 B 10 2

52 & s 5 N
Find number of permutations where: 8 & m 3 N n = 8, r = 3 These operations do not require you to press N to complete. To Square 6.3
39.69 3.94 0.31 120.00 5.32

Find square root:

15.3.5 &g 203.45 >
Find reciprocal: 1/3.2 Find factorial: 5! Find natural logarithm: ln 203.45

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.
n! nPr = -----------------( n r )!

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 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 on page 5.) For example, to enter 3 Q 10 3, 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 on page 80.) 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 (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 From Memory

To recall a number stored in memory, press J and a numeric key (09). Note: The recalled number remains in memory.

Memory Examples

To Clear memory 4 (by storing a zero value in it) Store 14.95 in memory 3 (M3) Recall a value from memory 7 (M7) Press

&w &r

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 (xP/Y, P/Y, 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.
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 on page 22.) Indicators prompt you to select settings, enter values, or compute results. For example, the i# $ indicators remind you to press # or " to select other variables. (See Reading the Display on page 2.) 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 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 press %. The calculator computes and displays the value based on the values of other variables.

TVM and Amortization Worksheet Variables
Variable Number of periods Interest rate per year Present value Payment Future value Key ,. / 0 Display Type of Variable
N I/Y PV PMT FV P/Y C/Y END BGN P1 P2 BAL PRN INT
Enter-or-compute Enter-or-compute Enter-or-compute Enter-or-compute Enter-or-compute Enter-only Enter-only Setting Setting Enter-only Enter-only Auto-compute Auto-compute Auto-compute
Number of payments per year & [ Number of compounding periods per year End-of-period payments Beginning-of-period payments Starting payment Ending payment Balance Principal paid Interest paid # &] &V &\ # # # #
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 (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, press %, 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

N I/Y PV PMT FV P/Y C/Y

Default 1

Variable

END/BGN P1 P2 BAL PRN INT

Default

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.

Press # to display each of the automatically computed values for
BAL, PRN, and INT in the next range of payments.
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 Set payments per year to 12. Press & [ 12 !

12.00 0.00 N= 360.00

Return to standard-calculator & U mode. Enter number of payments 30 & Z , using the payment multiplier.
To Enter loan amount. Enter payment amount. Compute interest rate.
75000. 425.84 S / 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 Set payments per year to 12. Press & [ 12 !
12.00 0.00 N= I/Y= PV= PMT= 360.00 5.50 75,000.00 -425.84
Return to standard-calculator & U mode. Enter number of payments using payment multiplier. Enter interest rate. Enter loan amount. Compute payment.

30 & Z , 5.5 75000.

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 Set payments per year to 4. Return to standard-calculator mode. Enter number of payments using payment multiplier. Press &[ 4 ! &U

30 & Z , N= P/Y=

4.00 0.00 120.00

To Compute payment.

Press %/

-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 Set all variables to defaults. Enter number of payments. Enter interest rate. Enter beginning balance. Compute future value. Press &} !
20 ,.S. RST N= I/Y= PV= FV=
0.00 20.00 0.50 -5,000.00 5,524.48
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 Enter final balance. Compute present value. Press

FV= PV=

10,000.00 -9,050.63
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 discount rate of 10%, what is the present value of the savings using an ordinary annuity and an annuity due?

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. 2. 3. 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 C02. Press & X. 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 (NPV) is the total present value of all cash flows, including inflows (cash received) and outflows (cash paid out). A positive NPV value indicates a profitable investment.
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. 2. 3. 4. Press ( to display the current discount rate (I). Key in a value and press !. Press # to display the current net present value (NPV). To compute the net present value for the series of cash flows entered, press %.

Computing IRR

1. 2. Press ). The IRR variable and current value are displayed (based on the current cash-flow values). 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 IRR solution exists. The calculator displays Error 5.
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.
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 find IRR, even if a solution exists. In this case, the calculator displays Error 7 (iteration limit exceeded).

Computing Statistical Results
Selecting a Statistics Calculation Method
1. 2. 3. 4. 5. Press & k to select the statistical calculation portion of the Statistics worksheet. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). Press & V repeatedly until the statistics calculation method you want is displayed. If you are analyzing one-variable data, select 1-V. 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 values for n, v, Sx, sX, GX, and GX2.

Computing Y'

1. 2. 3. 4. 5. To select the Statistics worksheet, press & k. Press " or # until X' is displayed. Key in a value for X' and press !. Press # to display the Y' variable. Press % to compute a predicted Y' value.

Computing X'

1. 2. 3. 4. 5. To select the Statistics worksheet, press & k. Press " or # until Y' is displayed. Key in a value for Y' and press !. Press " to display the X' variable. Press % to compute an X' value.

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 Old value/Cost New value/Selling price Percent change/Percent markup Number of periods Key &q # # # Display

OLD NEW %CH #PD

Variable Type Enter/compute Enter/compute Enter/compute Enter/compute
Note: This guidebook categorizes variables by their method of entry. (See Types of Worksheet Variables on page 17.)
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

OLD NEW

Default 0 0

%CH #PD

Default 0 1
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 #PD=1). A positive percent change 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

Computing Values

1. 2. To select the Percent Change/Compound Interest worksheet, press & q. The current value for OLD is displayed. To clear the worksheet, press & z.
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.
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 Select Percent Change/Compound Interest worksheet. Enter original forecast amount. Enter actual amount. Compute percent change. Enter -7 as percent change. Compute new actual amount. Press &q
OLD= OLD= NEW= %CH= %CH= NEW= 0 658.00 700.00 6.38 -7.00 611.94

# 700 ! #%

"%
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
OLD= OLD= NEW= 0 500.00 750.00 71
Select Percent Change/Compound & q Interest worksheet. Enter stock purchase price. Enter stock selling price.

Other Worksheets 500 !

# 750 !
To Enter number of years. Compute annual growth rate.

Press ## 5 ! "%

#PD= %CH= 5.00 8.45
Answer: The annual growth rate is 8.45%.
Example: Computing Cost-Sell-Markup
The original cost of an item is $100; the selling price is $125. Find the markup. To Select Percent Change/Compound Interest worksheet. Clear worksheet variables. Enter original cost. Enter selling price. Compute percent markup.

R A - AI = PAR ---- -M E

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

Depreciation

RDV = CST N SAL N accumulated depreciation
Values for DEP, RDV, CST, and SAL are rounded to the number of decimals you choose to be displayed. In the following formulas, FSTYR = (13 N MO1) P 12.
Straight-line depreciation
CST SAL -------------------------LIF First year: -------------------------- FSTYR
Last year or more: DEP = RDV

CST SAL LIF

Sum-of-the-years-digits depreciation
LIF + 2 YR FSTYR ) ( CST SAL ) ----------------------------------------------------------------------------------------------------( ( LIF ( LIF + 1 ) ) 2 ) First year: ----------------------------------------------------------- FSTYR
LIF ( CST SAL ) ( ( LIF ( LIF + 1 ) ) 2 )
Declining-balance depreciation
RBV DB% -----------------------------LIF 100

where: RBV is for YR - 1

First year: ------------------------------ FSTYR Unless ------------------------------ > RDV ; then use RDV Q FSTYR
If DEP > RDV, use DEP = RDV If computing last year, DEP = RDV

CST DB% LIF 100

Statistics
Note: Formulas apply to both x and y. Standard deviation with n weighting (s x):
x 2 ------------------x n ---------------------------------------n
Standard deviation with n-1 weighting (s x):
x x 2 ------------------n ---------------------------------------n1

Mean: x = -------------n

Regressions
Formulas apply to all regression models using transformed data.
n ( xy ) ( y ) ( x ) b = -------------------------------------------------------2 n ( x2 ) ( x ) ( y b x) a = -------------------------------n b x r = ------y
Interest Rate Conversions
EFF = 100 ( e C Y In ( x 1 ) 1 )

where: x =.01 Q NOM P CY

NOM = 100 C Y ( e 1 C Y In ( x + 1 ) 1 )

where: x =.01 Q EFF

Percent Change
%CH NEW = OLD 1 + ------------- 100
where: OLD =old value NEW =new value %CH =percent change #PD =number of periods

Profit Margin

Selling Price Cost Gross Profit Margin = ----------------------------------------------- 100 Selling Price

Breakeven

Out of range

Error 5
Possible Causes TVM worksheet: the calculator computed I/Y when 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 IRR without at least one sign change in the cash-flow list. 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. TVM worksheet: the calculator computed I/Y for a 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. TVM worksheet: $ was pressed to stop the evaluation of I/Y. Amortization worksheet: $ was pressed to stop the evaluation of BAL or INT. Cash Flow worksheet: $ was pressed to stop the evaluation of IRR. Bond worksheet: $ was pressed to stop the evaluation of YLD. Depreciation worksheet: $ was pressed to stop the evaluation of DEP or RDV.

No solution exists

Error 6

Invalid date

Error 7

Iteration limit exceeded

Error 8
Canceled iterative calculation

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 calculators accuracy. Additional calculations use the internal value, not the value displayed.

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. 1P3Q3=? Internally, the calculator solves the problem in two steps, as shown below. 1. 2. 1 P 3 = 0.3333333333333 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 1 (highest) (lowest) Operations
x2, x!, 1/x, %, nCr, nPr Yx
x, LN, e2, HYP, INV, SIN, COS, TAN

+, ) =

Battery Information

Replacing the Battery

Replace the battery with a new CR2032 lithium battery. Caution: Risk of explosion if replaced by an incorrect type. Replace only with the same or equivalent type recommended by Texas Instruments. Dispose of used batteries according to local regulations. Note: The calculator cannot retain data when the battery is removed or discharged. Replacing the battery has the same effect as resetting the calculator. 1. 2. 3. 4. 5. Turn off the calculator and turn it over with the back facing you. Using a small Phillips screwdriver, remove the four screws from the back cover. Carefully pry off the back cover. Using a small Phillips screwdriver, remove the screws from the metal battery cover and lift the cover off the battery. Tip the calculator slightly to remove the battery. Caution: Avoid contact with other calculator components. 6. 7. 8. Install the new battery with the positive sign (+) sign down (not showing). Replace the battery cover and the screws that hold it in place. Align the screw holes in the back cover with those in the calculator, then snap the back cover onto the calculator. Replace the screws.
Caution: Risk of explosion if replaced by an incorrect type. Replace only with the same or equivalent type recommended by Texas Instruments. Dispose of used batteries according to local regulations.

Battery Precautions

Do not leave battery within the reach of children. Do not mix new and used batteries. Do not mix rechargeable and non-rechargeable batteries. Install battery according to polarity (+ and - ) diagrams. Do not place non-rechargeable batteries in a battery recharger. Properly dispose of used batteries immediately. Do not incinerate or dismantle batteries. Seek Medical Advice immediately if a cell or battery has been swallowed. (In the USA, contact the National Poison Control Center collect at 202-625-3333.) Used only for small button cell batteries.

Battery Disposal

Do not mutilate, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Discard used batteries according to local regulations.

Australia & New Zealand Customers only
This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction. Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in duration to the above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or damages incurred by the consumer or any other user. Except as expressly provided in the One-Year Limited Warranty for this product, Texas Instruments does not promise that facilities for the repair of this product or parts for the repair of this product will be available. Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI's option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. The software and any documentation supplied with this product are protected by copyright.

All Other Customers

For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.

REVIEW OF CALCULATOR FUNCTIONS FOR THE TEXAS INSTRUMENTS BA II PLUS@
Samuel Broverman, University of Toronto
This note presents a review of calculator financial functions for the Texas Instruments BA II PLUS calculator. This note, including a number of the examples used as illustrations, is reprinted with permission from the 3rd edition of the book Mathematics of Investment and Credit, by S. Broverman. Also, several examples from SOA/CAS math of finance exams (old Course 2) will be presented illustrating the use of the calculator. A detailed guidebook for the operation of and functions available on the BA II PLUS can be found at the following internet site: http://education.ti.com/us/globallguides.html#finance. It will be assumed that you have available and have reviewed the appropriate guide book for the calculator that you are using.
Financial functions will be reviewed in the order that the related concepts are covered in Chapters 1 to 8 of Mathematics of Investment and Credit. Some numerical values will be rounded off to fewer decimals than are actually displayed in the calculator display.
It will be assumed that unless indicated otherwise, each new keystroke sequence starts with clear registers. Calculator registers are cleared with the keystroke sequences j2ndllCLR WORK

CE/C and

12ndllCLR TVMllcE/cl. It will also be assumed that the calculator is operating in US date format and US commas and decimals format, with the display showing 9 decimals. These are the default settings for the calculator, but they can be changed in the "FORMAT" work sheet, which is accessed with the keystroke sequence 12ndIIFORMATI. Although the number of decimals to display is set to 9, in the examples below it will often be the case that dollar amounts are written as rounded to the nearest.01.
CHAIN (CHN) AND ALGEBRAIC OPERATING (ADS) SYSTEM MODES
When the calculator is operating in chain calculation mode, the usual algebraic order of operations is not respected. For instance, the keystroke sequence 1+ 2 x 3 I;] results in an answer of 9. This is true because the calculation of 1+ 2 is performed first, resulting in 3, which is then multiplied by 3, resulting in 9. When the calculator is in AOS mode, the result of the keystroke sequence above will be 7. This is true because in the hierarchy of algebraic operations, multiplication is done before addition, so 2 x 3 is calculated first, resulting in 6, and then the addition operation is applied resulting in I + 6, which is 7. The order of operations mode can be selected in the "FORMAT" worksheet.
ACCUMULATED AND PRESENT VALUES OF A SINGLE PAYMENT USING A COMPOUND INTEREST RATE
Accumulated values and present values of single payments using annual (or more general periodic) effective interest rates can be determined using the calculator functions as described below.
ACCUMULATED VALUE: We use Example 1.1 to illustrate this function. A deposit of 1000 made at time 0 grows at effective annual interest rate 9%. The accumulated value at the end of 3 years is 1000(1.09)3 =1,295.03. This can be found using the calculator in two ways. 1. We use standard arithmetic operators with the following keystrokes. in standard calculator mode
1.09 [Z] 3 I;] @ 1000 I;] The screen should display 1,295.029.In this function, y=I.09 and x=3. 2. We use time value of money functions (TVM). 12ndilPNI ill I (this sets 1 compounding period per year).
12ndilQUITI (this returns calculator to standard-calculator mode)
1000 Ipvl (this sets PV to 1000), 9 Iwl (this sets the annual interest rate at 9%)
(this sets the number of years to 3),
ICPTIIFVI (this computes the accumulated value, also called future value). The screen should display -1,295.029. The calculator interprets the PV of 1000 as an amount received (a cash inflow) and the FV as the amount that must be paid back (a cash outflow), so the FV is a "negative" cashflow. If the PV had been entered as -1000, then FV would have been positive. This is part of the "sign convention" used by the BA II PLUS.
PRESENT VALUE: We use Example 1.5(a) to illustrate this function. The present value of 1,000,000 due in 25 years at effective annual rate.195 is 1,000,000i5 = 1,000, 000(1.195f25 = 11,635.96. This can be found using the calculator in two ways:

1. 1.195!Z] 25 1+/-1 g GJ 1000000g
The screen should display 11,635.96. This keystroke sequence can be replaced by:
1.195 11/ [ !Z] g GJ 1000000g x
2. Using time value of money functions, we have 12ndilPNI [I] I IENTER! 12nd! IQUIT!
1000000 IFVI19.5IWI 25 I.HJ ICPTllpvl. The screen should display -11,635.96. (the earlier comment about the negative value applies here). As a more general procedure, in the equation (PV)(I+i)N =FV, if any 3 of the 4 variables PV, i, N, FV are entered, then the 41hcan be found using the ICPTI function.
UNKNOWNINTEREST RATE: As an example of solving for the interest rate, we consider Example 1.5(c). An initial investment of 25,000 at effective annual rate of interest i grows to 1,000,000 in 25 years. Then 25,000(1+i)25 = 1,000, 000, from which we get i=(40)1/25 -1=.1590(15.90%). This can be found using the calculator power function with the following keystrokes: 40 I.2J.04

[;], the

screen should display 0.158997234.
Using financial functions, the keystroke sequence solving for i is 12ndilPNI ill 1 12ndilQUITI 1+/-IIFVI

25000 !PVll000000

25 [EJ ICPTI IINI The screen should display 15.89972344 (this is the % measure).

UNKNOWN TIME PERIOD:

As an example of solving for an unknown time period, suppose that an initial investment of 100 at monthly compound rate of interest i grows to 300 in n months at monthly interest rate i=.75%. Then 100(1.0075t =300, from

which we get n =

Inl~~75 = 147.03
months. This can be found using the
calculator ILNI function. Using financial functions, the keystroke sequence solving for n is
\2ndIIPN\ ill 1 12ndilQUITI 100 Ipvl 300 1+/-IIFVI.75 IINllcPT\ [EJ.
The screen should display 147.03026. Slightly more than 147 months of compounding will be required. The calculator returns a value of n based on compounding including fractional periods, so that the value of 147.03026 means that 100(1.0075)14703026 300. =
ACCUMULA TED AND PRESENT VALUES OF A SINGLE PAYMENT USING A COMPOUND DISCOUNT RATE
Present and accumulated values of single payments using an effective rate of discount can be made in the following way. Clear calculator registers before starting the keystroke sequence.
Present Value Usin!! a Compound Discount Rate: The present value of 500 due in S years at effective annual rate of discount 8% is 500(1-.08)8= 500(.92)8 = 256.61. This can be found using the calculator in a few ways: 1. We use standard arithmetic operators in standard calculator mode with the following keystrokes.
.92 !ZJ 8 ~ @ 500 The screen should display 256.61.

2. 500 IFVI 8 0

[!ZY] S 1+/-llliJIENTERljCPTllpvl
The screen should display -256.61. The calculator has calculated

= -FV(1+I)-N

= -500(1-.0Sr(-8)

= -500(.92)8 = -256.61.

(Remember the sign convention for payments in and payments out.) The following keystroke sequence could also be used.
3. 500jpvl sl+/-llwl 8 lliJICPTI!FVI
We have calculated - 500(1-.08)8

= -256.61.

Accumulated Value Usine: a Compound Discount Rate: A deposit of 25 made at time 0 grows at effective annual discount rate 6%. The accumulated value at the end of 5 years is

25(1-.06)-5

= 25(.94f5

=34.06

(nearest. 0 1).
This can be found using the calculator in two ways. 1. We use standard arithmetic operators in standard calculator mode with the following keystrokes.

.94[2] 5 1+/-1

~ ~ 25 ~
The screen should display 34.06 (rounded to nearest.01).

2. 25 Ipvl 61+/-1 lIlY

5 1+/-llliJlcPTIIFVI
The screen should display - 34.06 (negative sign indicating outflow). As a third approach, we could also find the effective annual interest rate and accumulate.
CONVERSION BETWEEN EFFECTIVE

ANNUAL AND NOMINAL RATES

The nominal annual interest rate compounded m times per year can be found from the effective annual rate of interest and vice-versa using calculator functions as illustrated below. Nominal Interest Rates A nominal annual interest rate of.24 (24%) compounded monthly is equivalent to an effective annual rate of interest of i =.2682 (26.82%).

The relationship i

= (1+ "12 )
-1 can be used, or the equivalent rates
can be found in the following way using the ICONV function.
Conversion from nominal annual to effective annual interest rate: We apply the following sequence of keystrokes. 12ndilICONVI

(NOM= appears),

24 ENTERI (the nominalrate) ill ill (CIY=appears)

121ENTER I (number of compounding periods),

ill ill (EFF= appears)

ICPTI.
The screen should display 26.82. We have converted the nominal annual interest rate of 24% (keyed in as 24) compounded monthly (keyed in as 12) to the equivalent effective annual interest rate of26.82%. Conversion from effective annual to nominal annual interest rate:
12ndilICONVI 26.82IENTER!

(EFF= appears)

ill (CIY= appears)
12 IENTER! ill (NOM= appears) ICPTI The screen should display 23.9966 (round to 24). We have converted the effective annual interest rate of 26.82% (key in 26.82) to the equivalent nominal annual interest rate compounded monthly (key in 12) of24%.
Nominal Discount Rates The nominal annual discount rate compounded m times per year can be found from the effective annual rate of interest and vice-versa using calculator functions as illustrated below.
A nominal annual discount rate of.09 (9%) compounded quarterly is equivalent to an effective annual rate of interest of i =.0953 (9.53%). The

relationship i

= (1 -
d~4)r4 -1 can be used, or the equivalent rate can be
found in the following ways.
Use the keystroke sequence 12ndilPNI 4 IENTERI12ndIIQUITI. This sets the number of compounding periods per year to 4 and returns to standard calculation functions. It is important to do this step first, entering the number of compounding periods in the year. I. We first find the equivalent effective annual rate of interest from the given nominal annual rate of discount. 41+/-1 [EJ 91+/-llwll

ICPTIIFVI

The display should read -1.0953; we interpret this as indicating that the effective annual rate of interest is 9.53%. We have calculated

-.09 1+4

= FV = -1.0953,
where P = 4 was entered with the PN function, N = -4 was entered with 41+/-1 [EJ,and 1=-.09 (or d=9%) wasenteredwith91+/-llwl.
2. We now find the equivalent nominal annual rate of discount from the given effective annual rate of interest. 41+/-1 [EJ, Key in 1.0953ll+/-IIFVI, Key in llpvl, Key inICPTIIINI. The display should read -9.00; this is the negative of the equivalent nominal annual rate of discount compounded 4 times per year.

Findin2 the Payment Amount: A loan of 1000 is to be repaid with monthly payments for 3 years at a compound monthly interest rate of.5%. The monthly payment is K

where 1000 = Ka361

. 005'
so that K = alOOO = 30.42.

'361.005

This can be found using the following sequence of keystrokes:

36 lliJ.5 IINIIENTERI

1000 Ipvl 0 IFVllcPTllpMTI
The display should read -30.42.
Findin2 the Interest Rate: Suppose that the loan payment is 35 for a 36 payment loan of amount 1000 and the interest rate is to be found. Then 1000 = 35ll36Ji' There is no algebraic solution for i. The following keystrokes give us i.
36lliJ 1000 1+/-1 Ipvl 35 IPMTI 0 IFVllcPTllwl
The display should read 1.31(%). That is the effective rate of interest per month.
Findin2 the Number ofPavments: We will use Example 2.13 to illustrate the calculator function for finding the unknown number of payments. In Example 2.13, Smith wishes to accumulate 1000 by means of semiannual deposits earning interest at nominal annual rate i(2) =.08, with interestcreditedsemiannually. In part (a) of Example 2.13, Smith makes deposits of 50 every six months. We wish to solve for n in the equation 1000 = 50. snJ.04.
The following keystrokes give us n. 1000 IFvl 50 1+/-llpMTI 41INI 0 IpvllcPTI [R]
The display should read 14.9866. 14 deposits are not sufficient and 15 full deposits are more than sufficient. The accumulated value of the deposits just after the 14thdeposit is 50,si4L04=914.60, so an additional deposit of 85.40 is needed at the time of the 14thdeposit to bring the total accumulated value to 1000. The accumulated value 6 months after the
14th deposit is 50. Si4l04

= 50(1.04)

. si4L04 = 951.18 ,
so a deposit of 48.18 is needed at time 15 to bring the accumulated value to 1000.
The next functions reviewed relate to finding the value of an annuity-due.
Annuitv-Due: The accumulated value and present value of a level payment annuity-due can be found using calculator functions. The same methods apply that were used for annuities-immediate, with the additional requirement that keystrokes 12nd!IBGNI12nd!ISETI!2ndIIQUITI must be entered to make the calculator view payments as being made at the beginning of each period (there is a screen indication of the BGN mode when it is invoked; when in BGN mode, in order to return to END mode, use the keystrokes !2ndIIBGNI12ndIISETI12ndIIQUITI, and BGN should disappear from the screen display, and the calculator is in END mode). In the equation PV = PMT. i:i:vJi'if any 3 of PV, PMT, N, i are entered, we can find the 4th.In the equation FV = PMT. sm; any 3 of FV, PMT, N, i are entered, we can fmd the 4th(as before, PMT and PV or FV are opposite signs). Findine the Time and Amount of a Balloon Payment: We can use the calculator functions to find the balloon payment required to repay a loan which has level payments for as long as necessary with a final balloon payment. In Example 2.15(a) of Chapter 2, a loan of5000 is being repaid by monthly payments of 100 each, starting one month after the loan is made, for as long as necessary plus an additional &actional

payment at the time of the final regular payment. At interest rate
=.09, we are to find the number of full paymentsthat are required
to repay the loan, and the amount of the additional fractional payment required if the additional fractional payment is made at the time of the final regular payment. We find the number of payments needed with the following keystrokes (the calculator should be in END mode). 5000 !PVllOO 1+/-llpMTI.75 IIIYllcPTllliJ The display should read 62.9. This indicates that the 62ndpayment is not quite enough to repay the loan. The additional payment needed, say X, at the time of the 62ndregular payment of 100 is found from the relationship X = 5000(1.0075)62 -100,s621.0075 = 89.55. The keystrokes that will produce the value of X are
5000 IpvllOO 1+/-llpMTI.75 IINI 62lliJlcPTIIFVI
The display should read -89.55.
ANNUITIES WHOSE INTEREST AND PAYMENT PERIODS DIFFER
A function is available to calculate annuity values when the interest period and payment period do not coincide. The following examples illustrate the use of this calculator function. I. Annuity-immediate of 10 annual payments of 1 each, with interest at a nominal annual rate of 8% compounded quarterly. The present value one year before the first payment is aiO!j' where

j = (1.02)4-I =.082432

is the effective annual rate of interest that is equivalent to the nominal
annual. The present value will be awJ.082432 6.6367. The annuity = value can be found using financial functions with the following sequence of keystrokes:
12nd! [lli] lIENTER! (this sets 1 payment per year),
ill 4 ENTER (this sets CN=4 interest conversion periods per

year), 12ndIIQUITI.

10 lliJ (10 annual payments),
8 I IIY (nominalannual interestrate of 8%), I 1+/-llpMTllcPTllpvl.
The display should read 6.637, the present value of the annuity. To find the accumulated value of the annuity, we continue with the followingkeystrokes: 0 Ipvl!cPTllFvl The display should read 14.655, the accumulated value of the annuity. Note that if we find the equivalent effective annual rate of interest first, i =.082432 , we could have found the annuity value as follows without setting CN to 4. This is done in the following way (CN and PN are both set to I). 10 lliJ (10 annual payments), 8.2432 lIlY (effective annual interest rate),

SDT=6-18-1990 (enter 6.1890), CPN=10, RDT=6-18-2010 (enter 6.1810), RV=100, ACT, 2N, bypass YLD=, PRI=150. Use ill to get to YLD= and then use ICPTI to calculate the yield rate. ;(2) The display should read 5.76 (YTM is =.0576, which is) = 2.88% every 6-months).
The previous calculations can also be done using the calculator annuity functions as follows. 12nd[ IPNI 2 IENTERI12nd[ !QUITI (ensures yield period and coupon period are the same). 40 lliJ (40 6-month periods), 5 Iwl (nominal annual yield rate), 5 1+/-llpMTI 100 I+/-IIFV[ (coupon payment every 6 months), (maturity value),
ICPTllpv[ should result in 162.76.
For the bond with maturity amount 110 we do the following. 40 lliJ 5 IllY I 5 1+/-llpMTIII0 This should result in 166.48. To find the yield rate for a price of 150 we do the following. 40 lliJ 150 Ipvl 5 1+/-llpMTII00 1+/-IIFVllcPTIIIIYI ]+/-IIFVllcPTllpvl
This should result in 5.76 (the nominal annual yield). Bond Amortization: The bond amortization components can be found using the calculator's amortization worksheet in much the same way they are found for loan amortization. A bond has face amount 1000, coupon rate 5% per coupon period, maturity value 1000, 20 coupon periods until maturity and yield-tomaturity 6% (per coupon period). The bond's amortized value just after the 5thcoupon is BVs

= 1000vI~6

+ 1000(.05).

a151.o6

= 902.88.
This can be found using the following keystrokes. 12ndllPIYll IENTERIIZndIIQUIT! 1+/-IIFVllcPTllpvl
ZO lliJ 6 IIIYI 50 1+/-llpMTIIOOO
The 20-year bond price of 885.30 should appear.
Then IZndllAMORTI should result in PI =. Key in 5]ENTERI ill. This should result in P2 =, and again enter 5 jENTERI. Then ill should result in 902.88, the balance just after the 5th coupon. Using the ill key again gives PRN=3.94, which is the negative of the principal repaid in the 5thpayment (the amount of write-up is 3.94, since the bond was purchased at a discount). Using the ill key again gives INT= - 53.94, which is the negative of the amount of interest due in the 5th payment.

Bond Price and Yield Between CouDon Dates: The bond examples considered so far have had valuation take place on a coupon date. It is also possible to use the bond worksheet functions to find the price (given the yield) or the yield (given the price) of a bond at any time, on or between coupon dates. We use Example 4.2 to illustrate the valuation of a bond between coupon dates. A bond has face amount 100, with an annual coupon rate of 10% and coupons payable semi-annually. The bond matures on June 18,2010 and is purchased on August 1,2000 at a yield rate of 5% (nominal annual yield compounded semi-annually). The quoted purchase price from Example 4.2 is 138.60. This can be found using the following keystrokes in the bond worksheet. SDT=8-01-2000 (enter 8.0100), CPN=10, RDT=6-18-2010 (enter 6.1810), RV=100, ACT, 2N, YLD=5 dENTERI must be used after each entry). At PR1=, use ICPTI to calculate the price. The display should read 138.60. Note that this is the quoted price which excludes the accrued coupon. The accrued coupon amount is found at AI=. If a price had been entered instead of a yield rate, we could have computed the yield.
INTERNAL RATE OF RETURN AND NET PRESENT VALUE
The internal rate of return for a series of payments received and payments made can be found in a couple of different ways, depending upon the nature of the series of payments. When we consider a level payment annuity with or without a balloon payment at the time of the last annuity payment, we can enter values into the variables
lliJ, Ipvl, IPMTI and IFvl, and then use !cPTI Iwl to find the
interest rate which satisfies the relationship PV

= PM!'.

a;;/j+ FV. vi.
The internalrate of return is).
We can use the cashflow worksheet (lCFI) to enter a cashflow at time 0, CFo, along with up to 24 additional cashflows at the end of 24 successive periods, CO1,CO2,., C24. Once these cashflow amounts are entered, we can use the IIRRI function (internal rate of return) to calculate an internal rate of return. It is a solution) to the relationship
CFo +C01'vj +C02.v; +.+C24.v;4
The cashflow amounts can each be positive (an amount received) or negative (an amount paid out). Calculatine Internal Rate of Return We illustrate how the internal rate of return in Example 5.1 can be found in this way. Example 5.1 has the following series of cashflows, where time is measured in 6-month intervals: Co = - 5100, C1 = 0, C2 = -2295, and C3 = 7982.5. The cashflow worksheet is cleared using ICFI12ndllCLR WORKI
The following series of keystrokes solves for the internal rate of return), where) will be the 6-month internal rate of return: Key inlCFI, the display should read CFo=, Key in 5100
ENTER III, the display should read CO1=,
Key in 0 ENTER III III, the display should read C02=, Key in IENTER I III III, the display should read C03=, Key in 7982.5 ENTER ,

We use Example 2.5 to illustrate this application. Suppose that 10 monthly payments of 50 each are followed by 14 monthly payments of 75 each. If interest is at a monthly effective rate of I%, what is the accumulated value of the series at the time of the final payment? The following keystrokes give us the accumulated value.

Key in 50 ENTER

[I] 10 ENTER
[IJ (this sets a payment amount of
C01=50 to be made for F01=10 successive periods), Key in 75 ENTER

[I] 14 jENTER

(this sets a payment amount of
C02=75 to be made for F02=14 successive periods after the first 10 periods). Key in INPvll jENTERI [IJ ICPTI
The screen should display 1,356.47. This is the present value of the 24 payments one month before the first payment. With NPV = 1,356.47 still displayed, Key in Ipvl. Key in 12ndilQUITI 24/R] I !INllcPTIIFVI This should result in the display FV = -1,722.36. This is the accumulated value of the series of24 payments at time of the final payment.
As a variation on Example 2.5, suppose that 10 deposits of 50 per month are made into an account earning monthly interest rate i. Suppose further that one month after the lOth deposit, monthly withdrawals are made from the account of amount 75 per month. The account balance is 0 just after the 14th withdrawal. We wish to find the monthly interest rate on the
account. We wish to solve for i in the equation 50siOli = 75aI4li'
This equation is equivalent to 50aiOli

= 75vlOaI4li'

We can place this in
the context of internal rate of return, where we wish to find the internal rate of return for a sequence of cashflows of 10 payments paid of 50 each (C01=50, F01=10) followed by 14 payments received of 75 each (C02=-75, F02=14), and whose total initial present value is CFO=O.
We use the following keystrokes:

0 ENTER

50 ENTER

10 ENTER

751+/-1 I ENTER ill 14IENTERIIIRRllcPTI.
The display should read IRR = 6.518.
EXAMPLES FROM SOAJCAS EXAM FM/2 (FORMERLYCOURSE2 COMPOUND INTEREST)
2003, #33 (Annuity Valuation)
At an effective annual interest rate of i, i > 0" both of the following annuities have a present value of X: (i) A 20-year annuity-immediate with annual payments of 55 (ii) A 30-year annuity-immediate with annual payments that pays 30 per year for the first 10 years, 60 per year for the second 10 years, and 90 per year for the final 10 years. Calculate X (A) 575

(B) 585

(C) 595

(D) 605

(E) 615

SOLUTION

The series of cashflows representing the difference between (i) and (ii) is a series of 10 payments of 55 - 30 = 25 each, followed by a series of 10 payments of 55 - 60 = - 5 each, followed by a series of 10 payments of -90 each. The interest rate that makes the present value of this series equal to 0 is found using the IRR function as follows. Key in
0 IENTER! ill 25 IENTER! ill 10 ENTER ,

ill 5 I+/-IIENTERI

ill 10 IENTER\,
ill 90 1+/-1 ENTER ill 10 IENTERI,
IIRRllcPTI. The display should read IRR = 7.177. This is the interest rate per year. Set PlY and CIY to 1. The following keystrokes give us the value of X 12ndilQUITI12ndllCLR 20 lliJ 7.177!wl TVMI

551+/-llpMTllcPTllpvl.

The display should read 574.74. Answer: A
is also Exercise 2.2.2) l.::t 2003, #8 (Annuity Valuation)J at (This beginning of each 4-year Kathryn deposits 100 into an account the
period for 40 years. The account credits interest at an effective annual interest rate of i. The accumulated amount in the account at the end of 40 years is.x; which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X (A) 4695

(B) 5070

(C) 5445

(D) 5820

(E) 6195
We denote the 4-year rate of interest byj. Then the accumulated value at the end of 40 years is X = 100siOlr (10 4-year periods, with valuation one full 4-year period after the 10th deposit). The accumulated value at the end of 20 years is 100s51r
Weare given that 100SiOlj

= 5 x 1OOs51j' which

is the same as

100SiOlj - 5 x 100s51j

(after we multiply both sides of the equations by Vj)' This can be interpreted as saying that 5 payments of 100 per period, followed by 5 payments of -400 per period has an accumulated value (and present value) ofO. We can use the IRR function to find} as follows. Key in
ENTER ill 100 ENTER ill 5 ENTER ,

400 1+/-1 ENTER I

ill5IENTERIIIRRllcPTI.
The display should read IRR = 31.95. The 4-year interest rate is } =.3195. Then we apply the following keystrokes. 12nd[IQUITI12ndIICLR TVMI
12nd[IBGNI12ndIISETI12ndIIQUIT/ 10 lliJ 31.95 IIN[ 100 IPMTllcPTI IFV[. Answer: E

The display should read -6,194.44.
into Fund X; which earns an effective annual rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an effective annual rate of 9%. Determine the accumulated value of Fund Yat the end of year 10. (A) 1519

'-=' 1000 is deposited

2003, #26 (Decreasing AnnUity~

(Exercise 2.3.13)

(B) 1819

(C) 2085

(D) 2273

(E) 2431

The 10 deposits to Fund Yare 160, 154, 148,., 112, 106. These can be entered as 10 separate cashflows in the ICFI worksheet. The NPV function at 9% will give a present value (one year before the deposit of 160) of 880.59. Then the FV at the end of 10 years will be 2,085. Answer: C
November2001,#16(Increasinf AnnUi~~

(Exercise2.3.12)

Olga buys a 5-year increasing annuity for X Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X (A) 2680

(B) 2730

(C) 2780

(D) 2830

(E) 2880
With monthly rate}, X = 2(Ia)601J' We are given 3-month rate.0225, so that (1+})3 = 1.0225, and therefore, ) =.007444. The numerator of (Ia)601i can be found by the following keystrokes.

12ndllBGNI[MJ ~

12ndllPNI12 IENTER

12ndilQUITI

[I] ICNI 4 IENTERI12ndIIQUITI,
60 [H] I 1+/-llpMTI 9jINI60 IFVllcPTI!pvl This results in the display reading PV = 10.1587. Then

.007444

~ 2 results in 2,729 on the display. Answer: B
John borrows 1000 for 10 years at an effective annual interest rate of 10%. He can repay this loan using the amortization method with payments of P at the end of each year. Instead, John repays the 1000 using a sinking fund that pays an effective annual rate of 14%. The deposits to the sinking fund are equal to P minus the interest on the loan and are made at the end of each year for 10 years. Determine the balance in the sinking fund immediately after repayment of the loan. (A) 213

2003, #25 (Loan Re~

(B) 218

(C) 223

(D) 230

(E) 237

P is found as follows. Clear all registers and be sure that IN and PN are both set to 1 and payment mode is END. Apply the following keystrokes. 10 lliJ 10 IINI1000 IpvllcPT!lpMT!
The screen displays -162.75. The deposits to the sinking fund are 62.75 each. The accumulated value of the sinking fund deposits at 14% is found as follows. 10 lliJ 141INI 62.75 IPMTI O!PVI!CPTIIFVI The display reads -1,213.42. After the principal loan amount of 1,000 is paid, 213 is left in the sinking fund. Answer: A
31 #42 , l.=r 2003,value (Bond Amortization)8% annual coupons is bought at a A 10,000 par 10-year bond with
premium to yield an effective annual rate of 6%.
Calculate the interest portion of the 7th coupon.

(A) 632

(B) 642

(C) 651

(D) 660

(E) 667

The AMORT functions can be used as follows.
10 lliJ 6 IINI 800 1+/-1+/-IIFVllcPTllpvl
The display reads 11,472.02 (the bond price). Then 12ndiiAMORTI 7 IENTER [

ill 7 ENTER ill

shows BAL = 10,534.60 (the book value after the ih coupon).
Then ill shows PRN = - 158.42 (the negative of the principal repaid), and ill shows INT = - 641.58 is the negative of the interest paid. Answer: B