Learning Objective

After studying this appendix, you should be able to:

[1] Use a financial calculator to solve time value of money problems.

Business professionals, once they have mastered the underlying concepts discussed in Appendix G, often use a financial calculator to solve time value of money problems. In many cases, they must use calculators if interest rates or time periods do not correspond with the information provided in the compound interest tables.

To use financial calculators, you enter the time value of money variables into the calculator. Illustration H-1 shows the five most common keys used to solve time value of money problems.¹

Illustration H-1
Financial calculator keys

where:

In solving time value of money problems in this appendix, you will generally be given three of four variables and will have to solve for the remaining variable. The fifth key (the key not used) is given a value of zero to ensure that this variable is not used in the computation.

Present Value of a Single Sum

To illustrate how to solve a present value problem using a financial calculator, assume that you want to know the present value of $84,253 to be received in five years, discounted at 11% compounded annually. Illustration H-2 depicts this problem.

Illustration H-2
Calculator solution for present value of a single sum

Illustration H-2 shows you the information (inputs) to enter into the calculator: N = 5, I = 11, PMT = 0, and FV = 84,253. You then press PV for the answer: –$50,000. As indicated, the PMT key was given a value of zero because a series of payments did not occur in this problem.

Plus and Minus Signs

The use of plus and minus signs in time value of money problems with a financial calculator can be confusing. Most financial calculators are programmed so that the positive and negative cash flows in any problem offset each other. In the present value problem above, we identified the $84,253 future value initial investment as a positive (inflow). The answer, –$50,000, was shown as a negative amount, reflecting a cash outflow. If the 84,253 were entered as a negative, then the final answer would have been reported as a positive 50,000.

Hopefully, the sign convention will not cause confusion. If you understand what is required in a problem, you should be able to interpret a positive or negative amount in determining the solution to a problem.

Compounding Periods

In the problem above, we assumed that compounding occurs once a year. Some financial calculators have a default setting, which assumes that compounding occurs 12 times a year. You must determine what default period has been programmed into your calculator and change it as necessary to arrive at the proper compounding period.

Rounding

Most financial calculators store and calculate using 12 decimal places. As a result, because compound interest tables generally have factors only up to five decimal places, a slight difference in the final answer can result. In most time value of money problems, the final answer will not include more than two decimal places.

Present Value of an Annuity

To illustrate how to solve a present value of an annuity problem using a financial calculator, assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12%, as pictured in Illustration H-3.

Illustration H-3
Calculator solution for present value of an annuity

In this case, you enter N = 5, I = 12, PMT = 6,000, FV = 0, and then press PV to arrive at the answer of –$21,628.66.

Useful Applications of the Financial Calculator

With a financial calculator, you can solve for any interest rate or for any number of periods in a time value of money problem. Here are some examples of these applications.

Auto Loan

Assume you are financing the purchase of a used car with a three-year loan. The loan has a 9.5% stated annual interest rate, compounded monthly. The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase. This problem is pictured in Illustration H-4.

Illustration H-4
Calculator solution for auto loan payments

To solve this problem, you enter N = 36 (12 × 3 years), I = 9.5, PV = 6,000, FV = 0, and then press PMT. You will find that the monthly payments will be $192.20. Note that the payment key is usually programmed for 12 payments per year. Thus, you must change the default (compounding period) if the payments are other than monthly.

Mortgage Loan Amount

Let's say you are evaluating financing options for a loan on a house. You decide that the maximum mortgage payment you can afford is $700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum home loan you can afford? Illustration H-5 depicts this problem.

Illustration H-5
Calculator solution for mortgage amount

You enter N = 180 (12 × 15 years), I = 8.4, PMT = –700, FV = 0, and then press PV. With the payments-per-year key set at 12, you find a present value of $71,509.81—the maximum home loan you can afford, given that you want to keep your mortgage payments at $700. Note that by changing any of the variables, you can quickly conduct “what-if” analyses for different situations.

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