FCL 345: Computer Applications in Finance
Calculators

Calculator Procedures for Hewlett-Packard Calculator, HP-10B

I. Basics

a. FV or Future Value Problem: If $500 investment earned an annual interest rate of 10 percent with annual compounding what would its' value be in five years?

Clear time value of money memory: 2^nd CLEAR ALL
Proper compounding: 2^nd P/Y = 1, enter, down arrow, C/Y = 1.

Enter number of years: n = 5
Enter interest rate: i = 10
Enter amount of investment: PV = 500 +/-
Not using payment key: PMT = 0
Calculate unknown: PRESS FV, answer is $805.26

b. Pv or Present Value Problem: What amount would have to be invested for five years, earning an annual interest rate of 10 percent, to have $805.26? In other words, what is the present value of 805.26 discounted back five years at an annual rate of 10 percent.

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter number of years: n = 5
Enter interest rate: i = 10
Enter Future Value: FV = 805.26
Not using payment key: PMT = 0
Calculate unknown: PRESS PV, answer is 500+/-

c. Unkown: n. How long must $500 remain invested, earning a 10 percent annual return, to grow to $805.26?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter interest rate: i = 10
Enter Present Value: PV = 500+/-
Enter Future Value: FV = 805.26
Not using payment key: PMT = 0
Calculate unknown: PRESS n, answer is 5.

d. Unkown: i. What annual percentage rate must $500 earn to grow to 805.26 at the end of 5 years.

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter Present Value: PV = 500+/-
Enter Future Value: FV = 805.26
Enter number of years: n = 5
Not using payment key: PMT = 0
Calculate unknown: PRESS i, answer is 10 percent

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III. Annuities. Time Value of Money Problems using multiple payments of equal value

a. Future Value of a Regular Annuity

What is the Future Value of 10 equal end of period payments of $100 each, invested at an annual interest rate of 10 percent

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter number of years: n = 10
Enter interest rate: i = 10
Enter payment: PMT = 100
Not using Present Value key: PV = 0
Calculate unknown: PRESS FV, answer is 1,593.742

b. Unkown: Number of years.

$1,593.74 is needed sometime in the future. How long, investing $100 per year, earning 10 percent annually, would it take to amass this amount of money?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter interest rate: i = 10
Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Not using Present Value key: PV = 0
Calculate unknown: PRESS n, answer is 9.999 (round to 10)

c. Unkown: Interest rate needed

Once again, $1,593.74 is needed, and you know ahead of time that you have 10 years to obtain it. What annual interest rate would a $100 annuity have to earn for you to achieve this goal?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: n = 10
Calculate unknown: PRESS i, answer is 9.999 (round to 10)

d. Unknown: Payment.

To obtain an amount of $2000.00 ten years from now, earning 10 percent annually, what amount would have to be invested on a yearly basis?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter Future Value: FV = 2000.00+/-
Enter Present Value: PV = 0
Enter number of years: n = 10
Enter interest rate: i = 10
Calculate unknown: PRESS PMT, answer is $125.49

e. Present Value of a Regular Annuity

What is the present value of a 4 year annuity, with payments of $100 earning 10 percent annually?

Clear time value of money memory: 2^nd CLEAR ALL   
Compounding should remain at P/Y = 1 and C/Y = 1

        Enter number of years: n = 4
        Enter Interest Rate: i = 10
        Enter Payments: PMT = $100+/-
        Enter Future Value: FV = 0
        Calculate unknown: PRESS PV, answer is $316.99

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*** The previous problems all deal with a regular annuities. The next set deals with an annuity due. The difference being that with an annuity due, payments are made at the beginning of the compounding periods.

IV. Annuities Due:  Time Value of Money Problems using equal beginning of period payments.

To change the setting on the calculator from regular to annuity due:
2^nd BGN, (BGN should appear in the lower middle of the display)

a. Unknown: FV or Future Value.

What is the Future Value of ten equal beginning of period payments of $100 each, invested at an annual interest rate of 10 percent.

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter number of years: n = 10
Enter interest rate: i = 10
Enter amount of payments: PMT = 100+/-
Enter Present Value: PV = 0
Calculate unknown: PRESS FV, answer is 1,753.12

b. Unknown: Number of years

$1,753.12 is needed sometime in the future. How long, investing $100 per year, earning 10 percent annually, would it take to amass this amount of money?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter interest rate: i = 10
Enter payment: PMT = 100+/-
Enter Future Value: FV = 1753.12
Not using Present Value key: PV = 0
Calculate unknown: PRESS n, answer is 10

c. Unkown: Interest rate needed

This time $1,500 is needed, and you know in advance that you have 10 years to obtain it. What annual interest rate would a $100 annuity due have to earn for you to achieve this goal?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter payment: PMT = 100+/-
Enter Future Value: FV = 1500.00
Enter Present Value: PV = 0
Enter number of years: n = 10
Calculate unknown: PRESS i, answer is 7.26 percent

d. Unknown: Payment

To obtain an amount of $3000.00 ten years from now, earning 10 percent annually, what amount would have to be invested on a yearly basis in an annuity due form?

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at P/Y = 1 and C/Y = 1

Enter Future Value: FV = 3000.00
Enter Present Value: PV = 0
Enter number of years: n = 10
Enter interest rate: i = 10
Calculate unknown: PRESS PMT, answer is $171.12+/-

e. Present Value of an Annuity Due

What is the present value of a 4 year annuity due, with payments of $100 earning 10 percent annually?

Clear time value of money memory: 2^nd CLEAR ALL   
Compounding should remain at P/Y = 1 and C/Y = 1

        Enter number of years: n = 4
        Enter Interest Rate: i = 10
        Enter Payments: PMT = $100+/-
        Enter Future Value: FV = 0
        Calculate unknown: PRESS PV, answer is $385.60

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V.  Loan Amortization

The loan amortization function is used to find the remaining balance, principle, and interest paid, of a loan with equal end of the month payments.  A 36 month loan with an initial balance of $20,000 and an effective monthly interest rate of 2.00% will be used. 

Step 1 will be to find the amount of the 36 equal monthly payments.

Clear time value of money memory: 2^nd CLEAR ALL
Compounding should remain at C/Y = 1, but P/Y needs to be changed to 12. To do this press 12, 2^nd, P/Y.

        Enter Present Value(Starting Balance): PV = 20,000
        Enter Future Value(Ending Balance): FV = 0
        Enter number of periods: n = 36
        Enter interest rate: i = 2
        Calculate unknown: PRESS PMT, answer is $784.657+/-

Step 2 will be to find the amount of the 12th payment allocated to interest and the amount allocated to principle.     

To amortize the 12^th payment, press 12, Input, 2^nd, Amort. The screen should read PEr 12-12.
Press and hold down the = key to show which portion of the payment will be displayed first.

The screen should now read 306.38, this is the amount of the payment assigned
to pay off interest.
Press the equal key again, the screen should now read 478.27, this is the amount of the payment assigned to principle.
Press the equal key again, the screen should now read 14,840.95, which is the remaining balance of the loan.
This can be used to find information on any payment in the sequence.   Just repeat the process inputting different period numbers.

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VI.  Interest Rate Conversion

The interest conversion function can be used when either the nominal interest rate is given, and the annual effective interest rate is needed, or when the annual effective rate is given and the nominal rate is needed.

a. A certificate offers a nominal interest rate of 5% with quarterly compounding. What is the annual effective interest rate?

This process can be reversed, for example, to find the Nominal rate when the Effective rate is given.

2. A certificate offers an annual effective interest rate of 6% with quarterly compounding. What is the nominal interest rate?

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XII.  NPV and IRR: Using the Cash Flow Register.

CFj: used to enter even or uneven cashflows.

2^nd, Nj: This is were the frequency of the cashflows will be entered, for example if a cashflow occurs twice in a row, you would enter 2, 2^nd, Nj.

2^nd, NPV: The NPV key is used to compute the net present value of a stream of cashflows. After the stream has been inputed, an interest rate must be entered into the I/YR key first to discount the cashflow. Once all the factors are present, the NPV can be computed.

2^nd, IRR/YR: This button is used to compute the internal rate of return. This being the rate at which the NPV equals zero.

Finding the NPV and the IRR of a stream of uneven cashflows.

Beginning with a cash outflow (investment) of $400, a project will result in 4 inflows of unequal amounts, spaced evenly, of 100, 200, 200, and 300 dollars. These cashflows will occur on a yearly basis.

Begin by clearing the register: 2^nd, CLEAR ALL.
Enter 1, 2^nd, P/Y to set the calculator to 1 period per year
400+/-, CFj (The screen should read CF 0 while the CFj button is depressed)
100, CFj
200, CFj
2, 2^nd, Nj (sets the frequency of the $200 payment at 2)
300, CFj

Now to obtain the answer, press 2^nd, IRR/YR and the answer should be 28.9. To calculate the NPV of this stream of cashflows, enter 10, I/YR for the discount rate, then 2^nd, NPV and 211.365 should appear as the Net Present Value of the stream.

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VIII.  Data Entry

To enter statistical data:

For one variable statistics, begin by pressing 2^nd CL Sum, this erases all previous data in the registry. Enter each value and press the Sum + key. After each value is entered the screen should display the total number of values contained in the registry (n).

The yearly return on the Market over a period of five years is given:

            Year                 Market Return
                1                          23.8%
                2                           (7.2)
                3                            6.6
                4                          20.5
                5                          30.6
               
Enter the data as follows:

X01 = 23.8
X02 = 7.2+/-
X03 = 6.6
X04 = 20.5
X05 = 30.6

Now that the single variable data has been entered, the next step is to perform the statistical calculations.

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IX.  Statistics

There are six keys which are used to do a statistical analysis on the HP 10B. They are accessed by pressing the recall button followed by the numerals 4 through 9. The keys are listed below.

2nd4- Estimate of X for a given value of Y
2nd5- Estimate of Y for a given value of X
2nd6- Mean of X weighted by Y
2nd7- Arithmetic mean of the X values
2nd8- Sample Standard Deviation of X values
2nd9- Population Standard Deviation of X values

More functions:
RCL4- Number of data points enterd
RCL5- Sum of the x-values
RCL6- Sum of the y-values
RCL7- Sum of the squares of the x-values
RCL8- Sum of the squares of the y-values
RCL9- Sum of the products of the x- and y-values

Since we have only entered figures for the x variable at this point, the only functions that will work will be 2nd 7, 8, and 9, and RCL 4, 5, and 7. 

(RCL4) Number of observations: n = 5
(2^nd7) Sample Mean: Xbar = 14.86
(2^nd8) Sample standard deviation: Sx = 15.11
(2^nd9) Population standard deviation: x = 13.52

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X.  Regression

To perform a Linear Regression analysis, a second  variable needs to be added.   In this case, the yearly return on Stock J. To enter x,y pairs of data, begin by clearing the contents of R4 through R9 by pressing 2^nd CLSum. Enter the first x variable and press input. Enter the y variable and press Sum +. The screen should read 1 indicating one pair of variable has been entered. Continue these steps until all variables have been entered.

     Year                   Return on Stock J  (Y variable)                      Market Return (X variable)
       1                          38.6%                                                                  23.8%
       2                         24.7+/-                                                                  7.2+/-
       3                          12.3                                                                      6.6
       4                            8.2                                                                      20.5
       5                          40.1                                                                      30.6

To perform two variable statistical analysis on this set of numbers, the commands explained in section X can be used. To find the regression variables:


Press 0 2^nd Yhat,m then press 2^nd SWAP
     a   = -8.922, b = 1.603
     To find the correlation coefficient
Press 2^nd Xhat,r then press 2^nd SWAP
correlation coefficient (r) = .913

Plugging these figures into the linear equation Y = a + bX we get Y = -8.922 + 1.603X, which can be used to predict a Y variable given the X variable and an X variable given a Y variable.  This can be done manually or the HP 10B will compute for you.

To estimate Y for a given X, enter the x-value and press 2^nd Yhat,m

Suppose the market is predicted to have a 10% return the following year.  Enter this as the X variable. The screen should display Y = 7.1089.  This would be the return on stock J if the predicted market return was correct. 

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Created by Roger Severance (Undergraduate Independent Study Project, 1998)
Last Updated on 4 June 1999
Email any comments to: robert.balik@wmich.edu