 
Calculating the Present Value of an Annuity
The basic steps in calculating the present value of an annuity are as
follows:
 Enter the Payments/Year
 Enter the rest of the information you know
 Solve for the unknown.
Let's try it with a problem
Suppose, you are interested in making an investment that pays $1,000 per
year at the end of the next five years. What should you pay for the investment
today if you wish to earn 8% annually on your investments?
First, let's see what we know
 We know that you will receive $1,000 at the end of the next five years.
That indicates that the Payment (PMT) is $1000 since it reoccurs every
period.
 We know that the number of years (xP/YR) is 5.
 We know that the annual interest rate is 8% (8 is the I/YR).
 Finally, we may assume that the periods per year is one since we are not
told it is monthly, quarterly, etc. (If the payments per year would have
been, for example, monthly, the problem would have read, ". . . earn 8% per
year, compounded monthly.")
Now let's compute the problem
 Enter the Payments/Year.
You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push
the orange
SHIFT key
,
then the P/YR key.
In our problem, first we must enter the appropriate payments per year by pushing 1, then
push the orange
SHIFT key
,
then the P/YR key
.
 Enter the rest of the information you know.
The order of the next three steps is not important, but I recommend that
you follow across the financial tour of your calculator from left to right.
 If
you do this, then the next step would be to enter in the proper number
of years. You first type the appropriate number, then push
the orange
SHIFT key
,
then the xP/YR
key.
In our problem, next we will enter the number of years by pushing 5,
then the orange
SHIFT key
,
then the xP/YR
key.
 Now, enter the appropriate interest rate per year. This is done by entering
the appropriate annual interest rate as a whole number, not as a decimal
(the calculator will convert it to decimal automatically), then pressing the
I/YR
key.
In our problem, now we will enter the interest rate per year by pushing 8 and then
pressing the I/YR
key.
 Next, enter the amount of the annuity (the payment that occurs every
period) and press the PMT
key.
In our problem, next we enter the Payment by pressing 1000, then the
PMT
key.
 Solve for the unknown.
Finally,
all that is necessary is push the PV
key to compute the answer.Correct Answer
The display then shows 3,992.71 if the display was set to show two
decimal places. Note that the answer is negative.
This indicates that the direction of the cash flow is out. (This is logical
if we will be getting $1000 per year for each of the next five years in the
future, we must pay $3,992.71 now.)
Would you like to review the mathematics of this
calculation?
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Copyright © 2005 Dr. Jerry D. Belloit
