Financial Calculator Supplement for Math for Business and Finance: An Algebraic Approach,1st Ed, by Jeffery Slater and Sharon Wittry.

The HP 10BII and TI BAII PLUS financial calculators are invaluable tools for the business student.  These tools will assist students in solving many common business problems.  It is important to remember that a financial calculator is only a tool used to assist in developing solutions to business problems.  A financial calculator is not a problem solver by itself.  As explained in the text, Time Value of Money problems can be solved using tables and formulae.  The financial calculator solves problems by calculating the values by using the appropriate TVM formula.

This supplement will cover Chapters 10 through 12 and Chapters 16 through 20 in Math for Business and Finance: An Algebraic Approach, 1st edition, by Jeffery Slater and Sharon Wittry.  Most of the examples and practical quiz problems are illustrated.  Selected end of chapter problems are also illustrated.  This supplement is divided into two sections. One section is devoted to the HP 10BII calculator and the other section covers the TI BAII PLUS calculator. 

HP 10BII Calculator

The HP 10BII comes complete with a users guide that explains in detail how this calculator works.  The guide also illustrates most of the calculator’s common applications.  It is a great resource, so it is wise to keep the user’s guide handy.

Hewlett-Packard Company has graciously given permission to use the User’s Guide and a photo of the HP 10BII.  Hewlett-Packard has asked that the following be included in this supplement.  (It’s a legal thing.)

Photos are the courtesy of Hewlett-Packard Development Company, L.P.

Hewlett-Packard does not warrant the accuracy or completeness of the material in this publication and disclaims any responsibility for it.

 

Please note the key I have labeled as the 2nd key.  HP calls this the shift key.  It is used to change the function of the various “function” keys on the calculator.  Function keys have a white function and an orange function.  To utilize the orange function, the 2nd or shift key must first be pressed.  Note that the display will show the word shift when the 2nd key is pressed.  This simply means you are using the orange functions rather than the white functions.  Try it.  Turn the calculator on by pressing the white ON key.  Turn the calculator off by pressing the 2nd key followed by the white ON key.  The calculator turns off because you are using the orange function which happens to be OFF.

Since most calculations are dollars and cents, it is a good practice to display the results to two decimal places.  This is accomplished by pressing the following keys;
2nd DISP (white “=” key) and 2.  The display will show 0.00. 

Unless otherwise instructed, your calculator should be set to 2 decimal places. 

It is important to note that the calculator’s register (memory) will retain the exact results of a calculation, regardless of the number of decimal places displayed.  The calculator register will retain at number such as 2.899523525689 even though the display shows 2.90.  If you wish to compute precise answers it will be important to use the number that resides in the calculator’s registry rather than rekeying a number as 2.90 instead of leaving the true value in the register. 

It is always a good idea to clear the display prior to starting a new operation.  Press the “C” key to clear the display and current register.  After pressing the C key, the register will display 0.00.

 

Chapter 10 - Installment Buying

Learning Unit 10-1 Cost of Installment Buying

Truth in Lending:  APR calculation, find APR when the amount financed and monthly payments are known. 

Note:  Payments are entered as a negative number because payments are cash outlays.  “N” represents the number of payments.  I/YR shows the periodic interest rate.  To change the periodic rate to an annual rate, multiply by 12.

Example: To calculate a payment amount when interest rate is known.

LU 10-1 Practice Quiz

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Chapter 11 - Discounts-Trade and Cash

A financial calculator can make calculating single trade discounts, chain (series) discounts, net price equivalents, and single equivalent discount rates much easier.  This section will acquaint you with your calculator and get you familiar with inputting different values and operations.

Learning Unit 11-1 Trade Discounts-Single and Chain

Single Trade Discount

Discount = List Price X Trade Discount Rate.

Find the discount for an item with a $5,678 list price and a 25% trade discount.

Note:  I show as the first step pressing the C or clear key.  This is to remind you that you need to clear the register prior to starting a new operation.

Finding Net Price for an item with a $2,700 list price and a 40% trade discount.

You don’t have to rekey numbers.  It is a good practice to use the numbers in the calculator’s display and register.  Whenever “~” is shown, the displayed number is used for the next function.  The word pend will show in the display during the continuous operation.  Pend disappears when the = key is pressed.  Pend denotes that the calculator has a pending operation.

Note:  For this step, you need to change the sign on the value in the register and then add it to another value to get the desired result.  For this step, press the +/– key followed by the + key.  I’ve separated the two keystrokes by a comma.  The comma is not keyed.

Calculating list price when net price and trade discount are known

The net price is $1,620 and the applied trade discount is 40%. 

By using the parenthesis, the division of $1,620 is delayed until the value of 1 minus .4 is determined.  Calculations within a set of parenthesis are performed first following the sequence of mathematical operations discussed earlier in your text.  The first parenthesis is the white “RM” key and the closing parenthesis is the white “M+” key.

Chain or Series Discounts

What is the net price for an item with a $15,000 list price and subjected to a 20/15/10 series discount.

Note 1:  In steps 3, 6, and 9 above, I separated the +/– and + keys with a comma.  Remember, the comma is not a keyed.  It is used simply to separate two distinct keystrokes.

Note 2:  Once again, the above series of calculations are performed without clearing the calculator’s register.  In this sequence, you are subtracting 3,000 from 15,000 and multiplying the results (12,000) times .15 to get the second discount amount of 1,800 as a continuous operation. 

Note 3:  There is no need to key trailing zeros.  If you feel more comfortable keying 10% as .10, then do so.  To save valuable time, you can skip keying the zero(s).  $2,500.00 can be keyed as 2500 or 2500.00.
Net Price Equivalent Rate

Calculating the net price equivalent rate is easily solved by using the calculator’s store and recall features.  Up to 10 different values can be stored in and recalled from memory.  To store a value, key the number, press 2nd STO, then press a number from 0 to 9.  To recall the stored value, press RCL and the number 0 to 9 that was used when the value was stored.  To clear stored values, press 2nd C ALL. 

What is the net price equivalent rate for a series discount of 20/15/10?

Note:  The number in the display is 0.61.  The number in the calculator’s register is actually 0.612.  0.612 is used for the last multiplication operation.

Single Equivalent Discount Rate

Using the steps above, calculate the Net Price Equivalent Rate.  Subtract this rate from 1.0.  Use the 2nd DISP function to set the number of decimal places needed to properly display the value. 

LU 11-1 Practice Quiz

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Note:  Since step 2 requires the use of this value, I simply stored it as stored number 4 and recalled the value when I needed it.  Use your imagination and creativity and let the calculator make your work easier. 

Solving a word problem with trade and cash discount.

Note:  The net price compliment is 1–.30 or .70 for the trade discount and 1–.02 or .98 for the cash discount.

LU 11-2 Practice Quiz

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Chapter 12 - Markups and Markdowns: Perishables and Breakeven Analysis

The HP 10BII has the ability to help you solve markup problems.  Four keys are used for these calculations. 
CST - $ cost of an item
PRC - $ selling price
MU - % markup on cost
MAR - % markup on selling price

Learning Unit 12-1 Markups based on cost

Situation #1 Where the cost of $18 and the selling price of $23 are known, find the markup on cost.

Note:  The display shows the markup as a whole number.  The value displayed (27.78) is read as 27.78% or .2778.

Situation #2 Where the cost of $100 and the markup on cost of 65% are known, find the selling price.

Situation #3 Where the selling price of $50 and the markup on cost of 40% are known, find the cost and dollar markup on cost.

LU 12-1 Practice Quiz

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Learning Unit 12-2 Markups based on selling price

Situation #1 Where the cost of $18 and the selling price of $23 are known, find markup on selling price.

Note:  Since we are now calculating markup based on selling price, the MAR key is used instead of the MU key.  Once again the MAR value is a percentage.  Two decimal places are inferred.

Situation #2 Where the cost of $100 and the markup on selling price of 65% are known, find the selling price and the dollar markup on selling price.

 

Input	Key(s)	Display
100	CST	100.00
65	MAR	65.00
	PRC	285.71
~	–	285.71
100	=	185.71

Situation #3 Where the selling price of $50 and the markup based on selling price of 40% are known, find the cost and the dollar markup on selling price.

LU 12-2 Practice Quiz

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Learning Unit 12-3 Markdowns and Perishables

Note:  Only 90% of the bagels are salable.  20 dozen times 90% is 18 dozen.

LU 12-3 Practice Quiz

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Note:  If 5% of the tomatoes will spoil, then 95% will be sold.

Learning Unit 12-4 Breakeven Analysis

LU 12-4 Practice Quiz

Selected End of Chapter Problems

12-4

12-7

12-9

12-20

12-25

 

Note: Since markup on Selling Price did not change, there is no need to rekey the 150%
(MAR key)
Chapter 16 - Simple Interest

Learning Unit 16-1 Calculation of Simple Interest and Maturity Value

Simple Interest Formula

I = PRT (Interest = Principal X Rate X Time)

What is the interest and maturity value of a $30,000 loan for 6 months at 8%?

I performed the calculation as one series of continuous actions.  The = key is only used when the final result is obtained.  There is no need to use the = key after each operation.  There is no need to rekey numbers on the display.  The word pend will show in the display during the continuous operation.  Pend disappears when the = key is pressed.  Pend denotes that the calculator has a pending operation. 

Simple Interest using the exact number of days

On March 4, Peg Carry borrowed $40,000 at 8% interest.  Interest and principal (MV) are due on July 6 (124 days). 

Simple Interest using Banker’s Interest (360 days)

LU 16-1 Practice Quiz

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Learning Unit 16-2 Finding Unknown in Simple Interest Formula

Finding the Principal

Principal = Interest ÷ (Rate X Time)

Tim Jarvis paid the bank $19.48 interest at 9.5% for 90 days.  How much did Tim borrow?

Note:  I show as the first step pressing the C or clear key.  This is to remind you that you need to clear the register prior to starting a new operation.  From this point forward I will assume that the register is cleared prior to starting an operation.

By using the parenthesis, the division of interest by rate times time is delayed until after the results of rate times time is determined.  Calculations within a set of parenthesis are performed first following the sequence of mathematical operations discussed earlier in the text.  The first parenthesis is the white “RM” key and the closing parenthesis is the white “M+” key.

Finding the Rate

Rate = Interest ÷ (Principal X Time)

Note: For this operation the answer required 4 decimal places.  The calculator was changed to four decimal places by pressing the 2nd key followed by DISP (white =) key followed by the number 4.

 

Finding the Time

Time = Interest ÷ (Principal X Rate)

Note:  I assume that the calculator has been reset to two decimals.  (Press 2nd DISP and the number 2).

LU 16-2 Practice Quiz

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Learning Unit 16-3 U.S. Rule—Making Partial Payments before Due Date

 

LU 16-3 Practice Quiz

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Note:  When doing a series of calculations where subsequent steps use the results of the previous step, there is no need to clear the display and rekey numbers.  Using numbers retained in the calculator’s register provides more accurate results.  Even if the calculator display is set to 2 decimals places, the register maintains the exact value not rounded to the displayed number.  This is, at least, the third or fourth time I’ve mentioned this point.  It’s very important that you get use to using the calculator’s registry value for continuous operations.

Chapter 17 - Promissory Notes, Simple Discount Notes, and the Discount Process

Learning Unit 17-1 Structure of Promissory Notes; The Simple Discount Note

The keystrokes for calculating interest and discount are virtually the same.  The difference is with the way interest is treated.  With simple interest loans, interest is added to principal to determine maturity value.  With discounted notes, the discount (interest) is subtracted from the principal to determine the proceeds.

LU 17-1 Practice Quiz

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2.  Retain 4 decimal places for this problem.

Learning Unit 17-2 Discounting an Interest Bearing Note Before Maturity

Example: Roger Company sold the following promissory note to the bank;

• Date of Note: March 8          
• Face Value of Note: $2,000
• Length of Note:  185 days
• Interest Rate: 10%
• Bank Discount Rate: 9%
• Date of Discount: August 9

Calculate Roger’s interest and maturity value.

Calculate bank discount and proceeds.

LU 17-3 Practice Quiz

Chapter 18 - The Cost of Home Ownership

Learning Unit 18-1 Types of Mortgages and the Monthly Mortgage Payment

Example:  Gary bought a home for $200,000.  He made a 20% down payment.  The 9% mortgage loan is for 30 years (360 payments).  What is the monthly payment?

If the interest rate drops to 7.5%, the payment would be:

Note:  Do not clear the calculator to adjust interest rate, number of payments, or amount financed.  Simply enter the new value(s) and press the PMT key.  The revised payment will appear.  This is very useful tool when comparing varying rates and terms.  You can always verify the values stored for each variable simply by pressing the variable’s key.  If you need to verify the interest rate currently stored in the calculator, press the I/YR key. 

LU 18-1 Practice Quiz

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Learning Unit 18-2 Amortization Schedule—Breaking Down the Monthly Payment

The amortization feature in the calculator allows you to calculate

• The amount applied to interest in a range of payments
• The amount applied to principal in a range of payments
• The loan balance after a specified number of payments are made

Assuming a $160,000 loan at 9% for 30 years

To break down individual loan payments or a range of loan payments, you must first enter the loan information as done above.  This establishes the values in the calculator’s register. 

To amortize a single payment, follow these steps;

For the first payment

Note: The display 1-1 AMORT-PER indicates that the amounts that follow are for payment 1 through payment 1, or the first payment. Each time the = key is pressed, the calculators toggles to the next value.  The values are displayed sequentially.  The first value is the principal portion of the payment.  The second value is the interest paid on the payment.  The third value is the principal balance that remains on the mortgage loan.

To find the amortized values for the first two payments, follow these steps

Note: The 1-2 AMORT-PER indicates that the values that follow are for payments one through 2.  The values are for all the payments in the range.

To amortize the first year worth of payments, follow these steps

After 12 payments, $1,093.17 of the principal is paid.  $14,355.63 in interest has been paid.  The balance on the $160,000 loan is $158,906.83.

Just for kicks, let’s amortize payment number 300

After 300 payments the loan balance is still $62,013.62 and you have already made payments totaling $386,220.00 on that $160,000 loan. 

 

 

Chapter 19 - Compound Interest and Present Value

In this and future chapters, we start to use the time value of money features of the financial calculator.  Time value of money (TVM) keys are the top row of keys on the HP 10BII.

The white key functions are;
N – Number of periods
I/YR – Interest rate per period
PV – Present Value
PMT – Payment
FV – Future Value
+/– – Changes displayed value to negative or positive amount
C – Clears the display

The orange or 2nd key functions are;
P/YR – Number of compounding periods per year (white PMT key)

BEG/END – Annuity payments are made at the beginning or end of a period.  The default setting is the end of the period.  If an annuity due is being calculated, the calculator must be set so payments are made at the beginning of the period.  Pressing the BEG/END (the white MAR key) will change the calculator from an ordinary annuity to an annuity due.  The word “BEGIN” will appear in the display.  If the word “BEGIN” is not in the display, annuity payments are assumed to be made at the end of the period (an ordinary annuity).

C ALL – Clears the TVM register.  Pressing 2nd C (the white C key) removes stored TVM amounts.  Pressing only the C key, without pressing the 2nd key first, only clears the display.  TVM amounts remain in the calculator’s register.

The calculator’s default setting is 12 periods per year.  Press 2nd C and watch the display.  “12 P _ Yr” appears briefly on the screen.  We need to change the calculator so that the N value we enter will represent one period and not 12.  To accomplish this simply enter;

Verify that the change has been made by clearing the TVM register (pressing 2nd and C).  The display will flash 1 P _ Yr. 

 Learning Unit 19-1 Compound Interest (Future Value) – The Big Picture

Example:  Bill Smith deposits $80 in a savings account for 4 years at an annual compound rate of 8%.  Find the value of the deposit in 4 years.

N = 4 years or periods
I/YR = 8% per period
PV = $80
FV = ? to solve, follow the steps below

Note: Always clear the TVM register before you start a new problem.  This way you are sure that no residual values reside in the register.  It’s a good practice.

When entering the interest rate, the calculator assumes the number entered is a percent.  The number 8 (entered above) is read by the calculator as .08.  If you would enter .08, the calculator would calculate future value using .08% or .0008.

Why was the present value entered as a negative number?  Good question.  Try to visualize the calculator as your wallet.  $80 was taken out of your wallet and invested at 8% for 4 years.  Therefore, the PV is entered as a negative number.  The FV is the amount received from the investment at the end of four years.  Hence it is a positive number.  If you were to input the PV as a positive number, the FV would display as a negative number.  The problem then could have been that you received $80 and paid out $108.84 at the end of the four years.  To keep things straight in you mind, continually think of your calculator as your wallet.  Whenever money is dispersed, input the amount as a negative number.

Example:  Find the interest on $6,000 at 10% compounded semiannually for 5 years.

Example:  Pam Donahue deposits $8,000 in her savings account that pays 6% interest compounded quarterly.  What will her balance be in 5 years?

Note:  This value differs from the amount shown using the compound interest table.  The calculator uses the exact values to calculate FV.  The table value of 1.3469 is rounded to four decimals.  The answers in this supplement will differ from the text because of this rounding error.  With large dollar amounts, large interest rates, and/or long periods of time, the difference between the values calculated using the compound interest tables and the calculator may be a significant amount.  Examples in the text will differ by a few dollars or cents.

Important note: Let the calculator compute the periodic interest rate.  6% compounded quarterly is 1.5% per period.  Entering 1.5 as the interest rate (I/YR) would give an accurate FV.  However, if the interest rate were 6.25%, using a periodic rate of 1.56 would not be accurate.  6.25 divided by 4 and rounded to 2 decimal places will display 1.56.  The actual periodic rate is 1.5625%.  By entering the interest rate as the annual rate divided by the number of compounding periods and pressing the I/YR key, the calculator uses the exact periodic rate and calculates an accurate FV.

Example: Find compounded (future) value of $900 in 25 years at 6% per year compounded daily, using a 360 day year.

Note:  Once again, the actual periodic rate is .016666667.  This is the rate the calculator used to solve for the FV even though the display showed .02.  If you had entered .02 as the interest rate, the FV would show to be $5,443.70, a significant difference, and a wrong answer.

 

LU 19-1 Practice Quiz

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Learning Unit 19-2 Present Value-The Big Picture

Example:  Rene Weaver needs $20,000 for college in 4 years.  She can earn 8% compounded quarterly at her bank.  How much must Rene deposit at the beginning of the year to have $20,000 in 4 years?

Note: PV is shown as a negative number because this is the amount that needs to be deposited (taken from your wallet).  You take $14,568.92 from your wallet, put it in the bank and in 4 years your balance will grow to $20,000.
LU 19-2 Practice Quiz

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Note: Amounts can be entered in any order.  You can put the FV in first, followed by the interest rate, then the number of periods.  The order of entry is irrelevant.  I find it a good habit to enter the figures in the same order.  For me, it’s less confusing.

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Selected Word Problems

19-11

19-14

 

There is no need to reenter the interest rate or number of periods since they remain constant.  Since the TVM register was not cleared, the periodic rate of 4.5% and the number of periods are maintained.  The PV value entered in steps 8 overrode the register amount.  A new FV is calculated using a PV of 59,533.90, at 4.5% for 6 periods.

19-20 Looking for PV

19-4 Looking for PV

 

Chapter 20 - Annuities and Sinking Funds

Learning Unit 20-1 Annuities: Ordinary Annuities and Annuity Due

Ordinary Annuity
Calculate the future value of an ordinary annuity with $3,000 annual payment at 8% in 3 years.

Note: Payments out are entered as negative numbers.  Payments received are positive numbers.  This is the same logic used for PV and FV calculations.

Annuity Due
Calculating the future value of an annuity due uses the same inputs as an ordinary annuity except the calculator is changed to the beginning mode.  Using the same $3,000, 3 year, 8% annuity, follow these steps;

Note: It is a good idea to reset the calculator to the normal or “end” mode after finishing an annuity due problem.  To do this, press the 2nd BEG/END.  The word BEGIN disappears from the display.

Example: Find the value of $3,000 quarterly payments earning 8% compounded quarterly in 3 years. 

To calculate this problem as an annuity due, where payments are made at the beginning of the period rather than the end, simply press the 2nd BEG/END key and the FV key.  The display will show 41,040.99.  You can toggle back and forth between an ordinary annuity and an annuity due simply by pressing the 2nd BEG/END key and the FV key.  The calculator remembers the interest rate, number of periods, and payment amounts until the 2nd C key is pressed. 

LU 20-1 Practice Quiz

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Learning Unit 20-2 Present Value of an Ordinary Annuity

Example: John wants to receive $8,000 payments at the end of each of the next 3 years.  John’s investment will pay 8% annually.  How much must John deposit to be able to make the desired withdrawals?

John must deposit $20,616.78 to receive 3 $8,000 ($24,000) annual payments.  The PV is negative because John must invest/deposit this amount.

Example:  John Sands made deposits of $200 semiannually to Floor Bank, which pays 8% interest compounded semiannually.  After 5 years, John makes no more deposits.  What will be the balance in the account 6 years after the last deposit? 

Step 1 Find the FV of the ordinary annuity.

Step 2 Find the FV of the above amount left on deposit for an additional 6 years.

Example:  Mel Rich decided to retire in 8 years to New Mexico.  What amount should Mel invest today so he will be able to withdraw $40,000 at the end of each year for 25 years after he retires?  Assume Mel can invest money at 5% compounded annually.

Step 1

Mel will need $563,757.78 in his annuity to receive the desired annual payments.

Step 2

Note: When moving from step 1 to step 2, there is no need to clear the calculator.  The PV for step 1 is a negative number representing an amount that must be invested to meet the annuity obligations.  For step 2, the negative PV is changed to a positive number and entered as the future value.  The amount needed in 8 years when Mel retires.  By entering 8 and pressing the “N” key, the 25 value entered in step 1 is overwritten with the 8 periods needed in step 2.  Since step 2 does not involve any payments, 0 is entered to overwrite the $40,000 payments used in step 1.  By pressing the PV key, the amount needing to be invested today to meet the annuity obligation is shown.  $381,576.46 needs to be deposited today to grow to $563,757.78 in 8 years so Mel can start making yearly withdrawals of $40,000 to fund his retirement. 

LU 20-2 Practice Quiz

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Learning Unit 20-3 Sinking Funds (Finding Periodic Payments)

Example: To retire a bond issue, Moore Company needs $60,000 in 18 years from today.  The interest rate is 10% compounded annually.  What payment must Moore make at the end of each year?

If the payments are made at the beginning of the year, the required sinking fund payment will change to the following.

LU 20-3 Practice Quiz

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To check this calculation

Selected End of Chapter Problems

20-10 Ordinary Annuity

20-15 PV of an Ordinary Annuity

20-21 Sinking Fund

20-25

Offer #1

 
Offer #2

Note: Since only the payment amount for the two annuities changed, I left the N and I/YR values in the register and simply recalculated PV using offer #2’s payment amount.

Cumulative Review

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TI BAII Plus Calculator

The Texas Instruments BAII Plus comes complete with a guidebook that explains in detail how this calculator works.  The guide also illustrates most of the calculator’s common applications.  It is a great resource, so it is wise to keep the user’s guide handy.

Texas Instruments has graciously given permission to use the guidebook and a photo of the BAII Plus.  Texas Instruments has asked that the following be included in this supplement.  (It’s a legal thing.)

Photo is the courtesy of Texas Instruments

Texas Instruments makes no warranty regarding the accuracy of the information presented in this document, including fitness for use for your intended purpose.  Also, TI is under no obligation to update the information presented in this supplement.

 

The BAII Plus has two modes of operation: the standard calculator mode and the prompted-worksheet mode.  The standard calculator mode is designed for time value of money (TVM) and standard math calculations.  The prompted worksheets guide you through advanced applications such as profit margin, cash flow and loan amortization calculations.  This supplement covers the loan amortization applications in Chapter 15 and profit margin or markup on selling price calculations in Chapter 8.

As you look at the BAII Plus notice there are words or symbols printed in yellow above most of the keys.  Most keys, therefore, have dual functions.  The white numbers, symbols, or words are considered the primary key function.  The yellow words and symbols are the secondary functions.  To use the secondary function, the yellow 2nd key is pressed prior to pressing the individual function key.  In this supplement, whenever the secondary function is to be used, I will indicate that the 2nd key is pressed first. 

The first step in understanding and using your calculator is to learn how to change the number of decimal places shown on the display.  Use the following keystrokes to change the number of decimal places;

Note: The default setting for the calculator is 2 decimal places.  Follow the above procedure to toggle between various decimal place settings.  Since most of your calculations will involve dollars and cents, it is advisable to leave your calculator with 2 decimal places showing. 

Please note that changing the number of decimal places only changes the display.  This procedure does not affect the number that is maintained in the calculator’s register.  The calculator’s register (memory) will retain the exact results of a calculation, regardless of the number of decimal places displayed.  The calculator register will retain a number such as 2.899523525689 even though the display shows 2.90.  If you wish to compute precise answers it will be important to use the number that resides in the calculator’s registry rather than rekeying a number as 2.90 instead of using the true value that is in the register.  Get in the habit of using the calculator’s register rather than rekeying numbers.

The CE/C key is used to clear the calculator.  Refer to the guidebook for a complete explanation of how to clear various functions from the calculator.  In the above example, pressing the CE/C once clears the secondary functions.  Pressing the CE/C key a second time clears the display.

 

 

 

 

 

 

 

Chapter 10 - Installment Buying

Learning Unit 10-1 Cost of Installment Buying

Truth in Lending:  APR calculation, find APR when the amount financed and monthly payments are known. 

Note:  Payments are entered as a negative number because payments are cash outlays.  “N” represents the number of payments.  I/Y shows the periodic interest rate.  To change the periodic rate to an annual rate, multiply it by 12.  Remember, 2 decimal places are inferred when using TVM.

Example: To calculate a payment amount when interest rate is known.

LU 10-1 Practice Quiz

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Chapter 11 - Discounts—Trade and Cash

A financial calculator can make calculating single trade discounts, chain (series) discounts, net price equivalents, and single equivalent discount rates much easier.  This section will acquaint you with your calculator and get you familiar with inputting different values and operations.

Learning Unit 11-1 Trade Discounts—Single and Chain

Single Trade Discount

Discount = List Price X Trade Discount Rate.

Find the discount for an item with a $5,678 list price and a 25% trade discount.

Note:  I show as the first step pressing the CE/C or clear key.  This is to remind you that you need to clear the register prior to starting a new operation

You don’t have to rekey numbers.  It is a good practice to use the numbers in the calculator’s display and register.  Whenever “~” is shown, the displayed number is used for the next function.

Finding Net Price for an item with a $2,700 list price and a 40% trade discount.

Note:  For this step, you need to change the sign on the value in the register and then add it to another value to get the desired result.  For this step, press the +/– key followed by the + key.  I’ve separated the two keystrokes by a comma.  The comma is not keyed.

Calculating list price when net price and trade discount are known

The net price is $1,620 and the applied trade discount is 40%. 

By using the parenthesis, the division of $1,620 is delayed until the value of 1 minus .4 is determined.  Calculations within a set of parenthesis are performed first following the sequence of mathematical operations discussed earlier in your text. 

Chain or Series Discounts

What is the net price for an item with a $15,000 list price and subjected to a 20/15/10 series discount.

Note 1:  In steps 3, 6, and 9 above, I separated the +/– and + keys with a comma.  Remember, the comma is not a keyed.  It is used simply to separate two distinct keystrokes.

Note 2:  Once again, the above series of calculations are performed without clearing the calculator’s register.  In this sequence, you are subtracting 3,000 from 15,000 and multiplying the results (12,000) times .15 to get the second discount amount of 1,800 as a continuous operation. 

Note 3:  There is no need to key trailing zeros.  If you feel more comfortable keying 10% as .10, then do so.  To save valuable time, you can skip keying the zero(s).  $2,500.00 can be keyed as 2500 or 2500.00.
Net Price Equivalent Rate

Calculating the net price equivalent rate is easily solved by using the calculator’s store and recall features.  Up to 10 different values can be stored in and recalled from the memory.  To store a value, key the number, press STO, then press a number from 0 to 9.  To recall the stored value, press RCL and the number 0 to 9 that was used when the value was stored.  To clear stored values, press 2nd MEM (the 0 key), 2nd CLR WORK (the CE/C key) and then CE/C. 

What is the net price equivalent rate for a series discount of 20/15/10?

Note:  The number in the display is 0.61.  The number in the calculator’s register is actually 0.612.  0.612 is used the for last multiplication operation.

Single Equivalent Discount Rate

Using the steps above, calculate the Net Price Equivalent Rate.  Subtract this rate from 1.0.  The first step is to set the number of decimal places needed to properly display the value. 

I keyed the CE/C key twice to clear all entries in the calculator’s register and return it to zero.
LU 11-1 Practice Quiz

1.

2.

3.

Note:  Since step 2 requires the use of this value, I simply stored it as stored number 4 and recalled the value when I needed it.  Use your imagination and creativity and let the calculator make your work easier. 

Learning Unit 11-2 Cash Discounts, Credit Terms, and Partial Payments.

Solving a word problem with trade and cash discounts.

Note:  The net price compliment is 1-.30 or .70 for the trade discount and 1-.02 or .98 for the cash discount.

LU 11-2 Practice Quiz

6.

Chapter 12 - Markups and Markdowns: Perishables and Breakeven Analysis

The TI BAII Plus has the ability to help you solve markup based on selling price.  Unfortunately, markup on cost will have to be done manually.  To calculate markup on selling price, you will use the calculator’s Profit Margin Worksheet.  To access this worksheet, press 2nd PROFIT
(the 3 key). 

To use the worksheet, you provide values for two of the three variables.  The calculator computes the third variable.  The three variables are:
CST = $ cost of an item
SEL = $ selling price of an item
MAR = % markup or profit margin.  Two decimal places are inferred.

The worksheet will be used to solve problems in LU 8-2.

Learning Unit 12-1 Markups Based on Cost

Situation #1 Where the cost of $18 and the selling price of $23 are known, find the markup on cost.

Since the desired answer is a percentage larger than two decimal places, the calculator needs to be set to the appropriate number of decimal places prior to starting the problem.

Situation #2 Where the cost of $100 and the markup on cost of 65% are known, find the selling price.

Prior to starting the problem, I reset the calculator to two decimal places.  This procedure was not shown.

 

 

Situation #3 Where the selling price of $50 and the markup on cost of 40% are known, find the cost and dollar markup on cost.

LU 12-1 Practice Quiz

1.

2.

3.

Learning Unit 12-2 Markups Based on Selling Price

Situation #1 Where the cost of $18 and the selling price of $23 are known, find markup on selling price.

The MAR value is a percentage.  Two decimal places are inferred.  The value 21.74 is read as 21.74% or .2174. 

CPT is the compute key.  Pressing CPT computes the unknown variable.

Pressing 2nd PROFIT starts the Profit Margin Worksheet.  From this point it is a matter of entering values for the three variables.  You toggle between the variables by using the ↓ and ↑ keys.

If values appear on the first screen after pressing 2nd PROFIT, simply press 2nd CLR WORK to clear the worksheet.

Situation #2  Where the cost of $100 and the markup on selling price of 65% are known, find the selling price and the dollar markup on selling price.

Keeping the calculator in the Profit Margin Worksheet mode,

Note:  Calculation can be made without exiting the worksheet mode.  This is denoted by the disappearance of the equals sign from the display.  Using the selling price of $285.71, I subtracted $100 (the cost) to arrive at $185.71.  Note that the equal sign is no longer displayed after I altered the selling price.  Press CPT and the calculated selling price is restored (SEL = 285.71)

Situation #3 Where the selling price of $50 and the markup based on selling price of 40% are known, find the cost and the dollar markup on selling price.

LU 12-2 Practice Quiz

1.

2.

3.                    

4.    

Markup on Cost

Markup on Selling Price

Learning Unit 12-3 Markdowns and Perishables

Pricing perishable items word problem

Note: Only 90% of the bagels are sold.  20 dozen times 90% is 18.

Learning Unit 12-4 Breakeven Analysis

LU 12-4

 

Selected End of Chapter Problems

 

12-7                           

12-9               

12-25

Chapter 16 - Simple Interest

Learning Unit 16-1 Calculation of Simple Interest and Maturity Value

Simple Interest Formula

I = PRT (Interest = Principal X Rate X Time)

 

It is always a good idea to clear the display prior to starting a new operation.  Press the CE/C key a couple times to clear the display and current register.   After pressing the CE/C key, the register will display 0.00.

Example:  What is the interest and maturity value of a $30,000 loan for 6 months at 8%?

 

Note that I performed the calculation as one series of continuous actions.  The”=” key is only used when the final result is obtained.  There is no need to use the “=” key after each operation.  There is no need to rekey numbers on the display. 

Simple Interest using the exact number of days

On March 4, Peg Carry borrowed $40,000 at 8% interest.  Interest and principal (MV) are due on July 6 (124 days). 

Simple Interest using Banker’s Interest (360 days)

LU 16-1 Practice Quiz

1. 

2.

3.

4.

5.

Learning Unit 16-2 Finding Unknown in Simple Interest Formula

Finding the Principal

Principal = Interest ÷ (Rate X Time)

Tim Jarvis paid the bank $19.48 interest at 9.5% for 90 days.  How much did Tim borrow?

Note:  I show as the first step pressing the CE/C or clear key.  This is to remind you that you need to clear the register prior to starting a new operation.  From this point forward I will assume that the register is cleared prior to starting an operation.

By using the parenthesis, the division of interest by rate times time is delayed until after the results of rate times time is determined.  Calculations within a set of parenthesis are performed first following the sequence of mathematical operations discussed earlier in your text. 

Interest is entered as .095 but the display shows 0.10 because the display is set to 2 decimal places.  Don’t worry, the calculator will use .095 when performing the calculation.

Finding the Rate

Rate = Interest ÷ (Principal X Time)

Note: For this operation the answer required 4 decimal places.  The calculator must be changed to four decimal places before doing the calculations. 

Finding the Time

Time = Interest ÷ (Principal X Rate)

Note:  I assumed that the calculator has been reset to two decimals.

LU 16-2 Practice Quiz

1.

2.

3.

Learning Unit 16-3 U.S. Rule—Making  Partial Payments

LU 16-3 Practice Quiz

1.

Note:  When doing a series of calculations where subsequent steps use the results of the previous step, there is no need to clear the display and rekey numbers.  Using numbers retained in the calculator’s register provides more accurate results.  Even if the calculator display is set to 2 decimals places, the register maintains the exact value not rounded to the displayed number.  This is, at least, the third or fourth time I’ve mentioned this point.  It’s very important that you get use to using the calculator’s registry value for continuous operations.

 

Chapter 17 - Promissory Notes, Simple Discount Notes, and the Discount Process

Learning Unit 17-1 Structure of Promissory Notes; The Simple Discount Note

The keystrokes for calculating interest and discount are virtually the same.  The difference is with the way interest is treated.  With simple interest loans, interest is added to principal to determine maturity value.  With discounted notes, the discount (interest) is subtracted from the principal to determine the proceeds.

LU 17-1 Practice Quiz

1.

2.  Retain 4 decimal places for this problem.

Learning Unit 17-2 Discounting an Interest Bearing Note before Maturity

Example: Roger Company sold the following promissory note to the bank;

• Date of Note: March 8          
• Face Value of Note: $2,000
• Length of Note:  185 days
• Interest Rate: 10%
• Bank Discount Rate: 9%
• Date of Discount: August 9

Calculate Roger’s interest and maturity value.

Calculate bank discount and proceeds.

 

LU 17-3 Practice Quiz

Chapter 18 - The Cost of Home Ownership

Learning Unit 18-1 Types of Mortgages and the Monthly Mortgage Payment

Example:  Gary bought a home for $200,000.  He made a 20% down payment.  The 9% mortgage loan is for 30 years (360 payments).  What is the monthly payment?

If the interest rate drops to 7.5%, the payment would be:

Note:  Do not clear the calculator to adjust interest rate, number of payments, or amount financed.  Simply enter the new value(s) and press the CPT and PMT keys.  The revised payment will appear.  This is very useful tool when comparing varying rates and terms. 

You can always verify the values stored for each variable simply by pressing the variable’s key.  If you need to verify the interest rate currently stored in the calculator, press the I/Y key. 

LU 18-1 Practice Quiz

1.

2.

Learning Unit 18-2 Amortization Schedule—Breaking Down Monthly Payments

The amortization feature in the calculator allows you to calculate

• The amount applied to interest in a range of payments
• The amount applied to principal in a range of payments
• The loan balance after a specified number of payments are made

Assuming a $160,000 loan at 9% for 30 years

To break down individual loan payments or a range of loan payments, you must first enter the loan information as done above.  This establishes the values in the calculator’s register.  You need to know the payment, term and principal before you can amortize the loan.

To amortize the loan, the Amortization worksheet is used.  To activate this worksheet, follow these steps;

For the first payment

Note:  The first display after pressing the 2nd AMORT keys is P1 = 1.00.  This indicates that the range of payments being amortized start with payment one.  Pressing the down arrow key will show the P2 value.  This is the ending period in the amortization range.  In the above example, we are amortizing payment one through payment one, the first payment.  The remaining amortization values are displayed sequentially by pressing the up or down arrow.  The first value displayed when the down arrow is pressed is the balance due on the note after the range of payments have been applied.  The second value is the amount of principal applied to the loan for the range of payments.  The third value is the amount of interest paid.

Pressing the C/CE key will take the calculator out of the loan amortization mode.  The display will show whatever value was on the screen when the C/CE key was pressed.  The loan values remain in the calculator’s register until the 2nd CLR TVM keys are pressed. 

To find the amortized values for the first two payments, follow these steps

To amortize the first year worth of payments, follow these steps (the steps assume that you have not cleared the amortization mode)

After 12 payments, $1,093.17 of the principal is paid.  $14,355.63 in interest has been paid.  The balance on the $160,000 loan is $158,906.83.

Just for kicks, let’s amortize payment number 300

After 300 payments the loan balance is still $62,013.62 and you have already made payments totaling $386,220.00 on that $160,000 loan. 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 19 - Compound Interest and Present Value

In this and future chapters, we start to use the time value of money features of the financial calculator.  Time value of money (TVM) keys are the third row of keys on the BAII Plus.  We will also be using the 2nd key and the CPT key.  CPT is short for compute.  The CPT key is located just above the 2nd key.

The white key functions are;
N – Number of periods
I/Y – Interest rate per period
PV – Present Value
PMT – Payment
FV – Future Value
+/– – Changes displayed value to negative or positive amount

The 2nd key functions are;
P/YR – Number of compounding periods per year (white I/Y key)

BGN – Annuity payments are made at the beginning or end of a period.  The default setting is the end of the period.  If an annuity due is being calculated, the calculator must be set so payments are made at the beginning of the period.  “BGN” will appear in the display when an annuity due is being calculated.  If the word “BGN” is not in the display, annuity payments are assumed to be made at the end of the period (an ordinary annuity).

CLR TVM – Clears the TVM register.  Pressing the 2nd  and the CLR TVM (the white FV) keys removes stored TVM amounts.  TVM amounts remain in the calculator’s register until they are cleared.

The calculator’s default setting is 12 periods per year.  We need to change the calculator so that the N value we enter will represent one period and not 12.  To accomplish this simply enter;

Your calculator should stay in the 1 period per year mode while working with this supplement. 
Learning Unit 19-1 Compound Interest (Future Value) – The Big Picture

Example:  Bill Smith deposits $80 in a savings account for 4 years at an annual compound rate of 8%.  Find the value of the deposit in 4 years.

N = 4 years or periods
I/YR = 8% per period
PV = $80
FV = ? to solve, follow the steps below

Note: Always clear the TVM register before you start a new problem.  This way you are sure that no residual values reside in the register.  It’s a good practice.

When entering the interest rate, the calculator assumes the number entered is a percent.  The number 8 (entered above) is read by the calculator as .08.  If you would enter .08, the calculator would calculate future value using .08% or .0008.

Why was the present value entered as a negative number?  Good question.  Here’s my answer.  Try to visualize the calculator as your wallet.  $80 was taken out of your wallet and invested at 8% for 4 years.  Therefore, the PV is entered as a negative number.  The FV is the amount received from the investment at the end of four years.  Hence it is a positive number.  If you were to input the PV as a positive number, the FV would display as a negative number.  The problem then could have been that you received $80 and paid out $108.84 at the end of the four years.  To keep things straight in you mind, continually think of your calculator as your wallet.  Whenever money is dispersed, input the amount as a negative number.

 

Example:  Pam Donahue deposits $8,000 in her savings account that pays 6% interest compounded quarterly.  What will her balance be in 5 years.

Note:  This value differs from the amount shown in the text using the compound interest table.  The calculator uses the exact values to calculate FV.  The table value of 1.3469 is rounded to four decimals.  The answers in this supplement will differ from the text because of this rounding error.  With large dollar amounts, large interest rates, and/or long periods of time, the difference between the values calculated using the compound interest tables and the calculator may be a significant amount.  Examples in the text will differ by a few dollars or cents.

Important Point:  Let the calculator compute the periodic interest rate.  6% compounded quarterly is 1.5% per period.  Entering 1.5 as the interest rate (I/YR) would give an accurate FV.  However, if the interest rate were 6.25%, using a periodic rate of 1.56 would not be accurate.  6.25 divided by 4 and rounded to 2 decimal places will display 1.56.  The actual periodic rate is 1.5625%.  By calculating the interest rate as the annual rate divided by the number of compounding periods and using this value for I/Y, the calculator uses the exact periodic rate and calculates an accurate FV.   Once again, let the calculator do the work.  Don’t rekey numbers.

Example: Find compounded (future) value of $900 in 25 years at 6% per year compounded daily, using a 360 day year.

Note:  Once again, the actual periodic rate is .016666667.  This is the rate the calculator used to solve for the FV even though the display showed .02. If you had entered .02 as the interest rate, the FV would show to be $5,443.70, a significant difference, and a wrong answer.

LU 19-1 Practice Quiz

1.

3.

Learning Unit 19-2 Present Value-The Big Picture

Example:  Rene Weaver needs $20,000 for college in 4 years.  She can earn 8% compounded quarterly at her bank.  How much must Rene deposit at the beginning of the year to have $20,000 in 4 years?

Note: PV is shown as a negative number because this is the amount that needs to be deposited (taken from your wallet).  You take $14,568.92 from your wallet, put it in the bank and in 4 years your balance will grow to $20,000.

LU 19-2 Practice Quiz

1.

Note: Amounts can be entered in any order.  You can put the FV in first, followed by the interest rate, then the number of periods.  The order of entry is irrelevant.  I find it a good habit to enter the figures in the same order.  For me, it’s less confusing.

2. 

3.

4.

Selected Word Problems

19-11

19-14

There is no need to reenter the interest rate or number of periods since they remain constant.  Since the TVM register was not cleared, the periodic rate of 4.5% and the number of periods are maintained.  The PV value entered in steps 10 overrode the register amount.  A new FV is calculated using a PV of 59,533.90, at 4.5% for 6 periods.

19-20 Looking for PV

19-24 Looking for PV

Chapter 20 - Annuities and Sinking Funds

Learning Unit 20-1 Annuities: Ordinary Annuities and Annuity Due

Ordinary Annuity
Calculate the future value of an ordinary annuity with $3,000 annual payment at 8% in 3 years.

Note: Payments out are entered as negative numbers.  Payments received are positive numbers.  This is the same logic used for PV and FV calculations.

Annuity Due
Calculating the future value of an annuity due uses the same inputs as an ordinary annuity except the calculator is changed to the beginning mode.  Using the same $3,000, 3 year, 8% annuity, follow the steps shown.  The first three lines will set the calculator to the beginning or annuity due mode.  After you have pressed 2nd BGN, every time 2nd ENTER is press, the calculator toggles between beginning and ending modes. 

Note: It is a good idea to reset the calculator to the normal or “end” mode after finishing an annuity due problem.  To do this, press the 2nd BGN followed by 2nd ENTER then CE/C.  After you press 2nd ENTER the word END will appear in the display.  The word BGN disappears from the display.  The word BGN will remain in the upper right corner of the display whenever the calculator is in beginning, annuity due mode.

Example: Find the value of $3,000 quarterly payments earning 8% compounded quarterly in 3 years. 

To calculate this problem as an annuity due, where payments are made at the beginning of the period rather than the end follow these steps;

Press 2nd BGN followed by 2nd ENTER
Then CE/C
Then CPT followed by FV
41,040.99 will appear along with the word BGN in the display. 

You can toggle back and forth between an ordinary annuity and an annuity due simply by following the above keystroke sequence.  The calculator remembers the interest rate, number of periods, and payment amounts until the 2nd CLR TVM keys is pressed. 

LU 20-1 Practice Quiz

1. 

2.  Calculator is set to beginning mode.

Learning Unit 20-2 Present Value of an Ordinary Annuity

Example: John wants to receive $8,000 payments at the end of each of the next 3 years.  John’s investment will pay 8% annually.  How much must John deposit to be able to make the desired withdrawals?

John must deposit $20,616.78 to receive 3 $8,000 ($24,000) annual payments.  The PV is negative because John must invest/deposit this amount.

Example:  John Sands made deposits of $200 semiannually to Floor Bank, which pays 8% interest compounded semiannually.  After 5 years, John makes no more deposits.  What will be the balance in the account 6 years after the last deposit. 

Step 1 Find the FV of the ordinary annuity.

 

 

Step 2 Find the FV of the above amount left on deposit for an additional 6 years.

Example:  Mel Rich decided to retire in 8 years to New Mexico.  What amount should Mel invest today so he will be able to withdraw $40,000 at the end of each year for 25 years after he retires?  Assume Mel can invest money at 5% compounded annually.

Step 1

Mel will need to start with $563,757.78 in his annuity to receive the desired annual payments.

Step 2

Note: When moving from step 1 to step 2, there is no need to clear the calculator.  The PV for step 1 is a negative number representing an amount that must be invested to meet the annuity obligations.  For step 2, the negative PV is changed to a positive number and entered as the future value.  The amount needed in 8 years when Mel retires.  By entering 8 and pressing the “N” key, the 25 value entered in step 1 is overwritten with the 8 periods needed in step 2.  Since step 2 does not involve any payments, 0 is entered to overwrite the $40,000 payments used in step 1.  By pressing the CPT and PV keys, the amount needing to be invested today to meet the annuity obligation is shown.  This is the amount that needs to be deposited today to grow to $563,757.78 in 8 years so Mel can start making yearly withdrawals of $40,000 to fund his retirement. 

LU 20-2 Practice Quiz

1.

2.

3.

Learning Unit 20-3 Sinking Funds (Finding Periodic Payments)

Example: To retire a bond issue, Moore Company needs $60,000 in 18 years from today.  The interest rate is 10% compounded annually.  What payment must Moore make at the end of each year?

LU 20-3 Practice Quiz

1.

To check this calculation

Selected End of Chapter Problems

20-10 Ordinary Annuity

Input	Key	Display
	2nd CLR TVM	0.00
800	+/–, PMT	PMT = –800.00
4	N	N = 4.00
4	I/Y	I/Y = 4.00
	CPT, FV	FV = 3,397.17

20-15 PV of an Ordinary Annuity

Input	Key	Display
	2nd CLR TVM	0.00
525	+/–, PMT	PMT = –525.00
4 X 12	=	48.00
~	N	N = 48
6 ÷ 12	=	0.50
~	I/Y	I/Y = 0.50
	CPT, PV	22,354.67

20-21 Sinking Fund

Input	Key	Display
	2nd CLR TVM	0.00
30000	FV	FV = 30,000.00
8 X 2	=	16.00
~	N	N = 16.00
12 ÷ 2	=	6.00
~	I/Y	I/Y = 6.00
	CPT, PMT	–1,168.56

20-25

                     Offer 1

Input	Key	Display
	2nd CLR TVM	0.00
35000	PMT	PMT = 35,000.00
5	N	N = 5.00
8	I/Y	I/Y = 8.00
	CPT, PV	PV = –139,744.85
~	+/–, +	139,744.85
40000	=	179,744.85

                     Offer 2

Input	Key	Display
38000	PMT	PMT = 38,000.00
	CPT, PV	PV = –151,722.98
~	+/–, +	151,722.98
25000	=	176,722.98

Since only the payment amount for the two annuities changed, I left the N and I/Y values in the register and simply recalculated the PV using the second PMT amount.