Calculating the Future Value of an Annuity

The basic steps in calculating the future 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 FV key.

Now let's try a problem. Consider that you invest $1000 in a bank account at the end of every year for 3 years. The bank will pay 8% annual interest on the deposits. How much would your bank account be worth at the end of the three years?

First let's see what we know. We know that there will be three deposits of $1000 at the end of each year for three years. That indicates that the payment (PMT) is $1000 since it is a recurring payment every period. We know that the number of years is 3. 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, ". . . pay 8% annual interest, 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 3, 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 key (to show that this is paid to the bank), and then the PMT key.
  5. Finally, we press the the FV key to compute the answer. The display then shows 3246.40 if the display was set to show two decimal places. Note that the answer is positive. This indicates that the direction of the cash flow is in. (This is logical since we pay $1000 per year in order to receive $3,246.40 in the future.)

Would you like to review the mathematics of this calculation?

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Copyright 2006  Dr. Jerry D. Belloit