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Calculating the Future Value of an Annuity

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

  1. Enter the Payments/Year
  2. Enter the rest of the information you know
  3. Solve for the unknown.

Let's try it with 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. 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 .
  2.  

  3. 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 3, 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 key (to show that this is paid to the bank), and then the PMT key.
  4.  

  5. Solve for the unknown.
    Finally, we press the the FV key to compute the answer.

    Correct Answer
    The display then shows 3,246.40 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 2005  Dr. Jerry D. Belloit