Recognizing the Different Types of Time Value of Money Problems.

Sometimes students feel overwhelmed when facing a time value of money word problem. Actually, solving a word problem is not as hard as you might think. If you follow the following steps, you will discover that solving a word problem is as easy as 1-2-3!

1. Read the problem and find out what it is that the problem is asking you to solve. This is called the unknown. It is usually the item that follows the "how" or "what" in the question. Common "how" questions are "how much . . .", "how long . . .", or "how many . . . ." Most "what" questions have the form "what is the . . ."
2. Identify all of the different types of information that is given.
 The payments per year (or the compounding period) is always given (or may be assumed to be annual if no period is mentioned.) Look for the words annually (1 P/YR), semi-annually (2 P/YR), quarterly (4 P/YR), bi-monthly (6 P/YR), monthly (12 P/YR), bi-weekly (26 P/YR), weekly (52 P/YR), or daily (365 P/YR). If more than one of these words is used in the problem, the payments per year is usually the largest number of payments per year. The number of years is usually easily recognized unless it the unknown sought in the problem. The present value (PV) will be that value which is the earliest in time. Sometimes it is easy to think that a reference to "today" suggests a present value. However, that is not always reliable. Consider the following problem: "If you purchased a lot for \$ 24,509 eleven years ago, what is your expected annual rate of return if you can sell the lot for \$ 90,558 today and you assume bimonthly compounding?" In this problem, \$24,509 is the present value since it occurred the earliest in time. The amount of the payment (PMT) is an amount which is repeated every period. (Remember that another name for this reoccurring payment is an annuity.) This means any payment amount must occur more than once in the problem. Just because you see the word "pay", you cannot assume that it refers to a payment unless it occurs more than once. For example, if the problem says "pay each month", this would be a payment. However, if it simply says "you pay \$10,000 for an investment that . . .", the \$10,000 would not be a payment since it the problem implies that there is only one \$10,000 payment. The future value (FV) will be that value which is the latest in time. Sometimes it is easy to think that a reference to "today" suggests a present value. However, that is not always reliable. Consider the problem cited above: "If you purchased a lot for \$ 24,509 eleven years ago, what is your expected annual rate of return if you can sell the lot for \$ 90,558 today and you assume bimonthly compounding?" In this problem, \$90,558 is the future value since it occurred the latest in time. Finally the interest rate per year (I/YR) must be on an annual basis. If the problem specifies an interest rate on other than an annual basis, you would need to convert the rate to an annual rate. For example, if the problem said "1% monthly interest", this would be entered as 12% annual interest.
3. Simply enter the given information into the calculator and solve of the unknown.

Let's try our 1-2-3 procedure on a few word problems.

First let's consider the problem mentioned above: "If you purchased a lot for \$ 24,509 eleven years ago, what is your expected annual rate of return if you can sell the lot for \$ 90,558 today and you assume bimonthly compounding?"

1. What is the problem is asking you to solve? Look for the "what is" in the problem. It asked, "what is your expected annual rate of return." Therefore, the problem is asking for an interest rate per year. You will be solving for I/YR.
2. Next, identify what you know.
 You are given an amount of \$24,509. This amount occurred first, so it is a present value (PV). You are given the number of years ("eleven years ago") as 11. You are given an amount of \$ 90,558. This amount occurred last so it is a future value (FV). Finally, you are told the compounding period (P/YR). In this case the problem says "bi-monthly" so your payments per year is 6. (Note that the problem mentions both the words annual and bi-monthly. Using the general rule suggested above, you would use the largest number of payments per year as the correct entry.)
3. Now enter the data and solve for the unknown.
 Remember you must always begin by entering the payments per year. You would do this by pressing 6, the cream colored key , and then the P/YR key. Now enter the number of years by pressing 11, the cream colored key , and then the xP/YR key. The present value is entered by pressing 24509, the change sign key, and then the PV key. The sign is changed to indicate that this cash flow was paid rather than received. The future value is entered by pressing 90558 and then the FV key. Finally, you solve for the unknown, the annual rate, by pressing the I/YR key. The display show 12. This means that you would have earned 12% per year on your investment.

Would you like to test your skill at recognizing the parts in a time value of money word problem?