# Calculating the Present Value of an Annuity

The basic steps in calculating the present value of an annuity are as follows:

1. Enter the proper payments per year. You first must type in the appropriate number (eg. monthly would be 12, quarterly would be 4, etc.), then push the cream colored key , then the P/YR key.
2. 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 cream colored key , then the xP/YR key.
3. 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.
4. Next enter the amount of the annuity (the payment that occurs every period) and press the PMT key.
5. Finally all that is necessary is push the PV key.

Now let's try 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:

1. First we must enter the appropriate payments per year by pushing 1, then the P/YR key.
2. Next we will enter the number of years by pushing 5, then the cream colored key , then the xP/YR key.
3. Now we will enter the interest rate per year by pushing 8 and then pressing the I/YR key.
4. Next we enter the Payment by pressing 1000, then the PV key.
5. Finally, we press the PV key to compute the answer. The display then shows -3992.71 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?