 
Recognizing the Different Types of Time
Value of Money Word 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 123!
 Read the problem and find out what it is that the problem is asking you to
solve.
 Identify all of the different types of information that is given.
 Simply enter the given information into the calculator and solve for the
unknown.
Let's try our 123 procedure on a word 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?"
 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 . . ."
What is the problem 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.
 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), semiannually
(2 P/YR), quarterly (4 P/YR), bimonthly
(6 P/YR), monthly (12 P/YR), biweekly
(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.
Consider
the problem mentioned above: You are given the bimonthly compounding. Therefore,
you enter 6 P/Yr.
 The number of years is usually easily recognized unless it the unknown
sought in the problem.
Consider the problem mentioned above: You are given the number of years ("eleven years ago")
as
11.
 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 problem mentioned above: You are given an amount of $24,509. This amount
occurred first, so it
is a present value (PV).
 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
the problem implies that there is only one $10,000 payment.
Consider
the problem mentioned above: There is no series of payments (reoccurring
payments)
involved here. Therefore, we don't have PMT in this problem.
 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 mentioned above: You are given an amount of $ 90,558. This amount
occurred last so it
is a future value (FV).
 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.
 Simply enter the given information into the calculator and solve for the
unknown.
 Remember you must always begin by entering the payments per year. You
would do this by
pressing 6 (since it is bimonthly compounding), the orange
SHIFT key
,
and then the P/YR
key.
 Now enter the number of years by pressing 11, the orange
SHIFT 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?
return to the top
return to Calculating
Specific Types of TimeValueofMoney Problem page
Send
mail to
Dr. Jerry Belloit with questions or comments about this web site.
Copyright © 2006 Dr. Jerry D. Belloit
