# Examples for How to Calculate Annuities

by Amanda McMullen

When you invest in an annuity, you create a savings account that will make payments to you in the future. However, to gain the maximum benefit from an annuity, you must compare your options before making an investment. Calculating the future values of different annuity options is one method you may use to compare the yields of two or more annuities.

## Formula for Future Value

To calculate the future value of an annuity, add 1.0 to the annuity's interest rate per period. Next, raise the result to the nth power, where "n" is the number of payments made into the annuity over time. Subtract 1.0 from this value, and then divide by the interest rate per period. Finally, multiply by the value of each payment made into the annuity.

## Example One

Assume you are investing \$8,000 each year in an annuity over a period of 10 years with an interest rate of 2 percent. The future value of your annuity is \$87,596. To calculate this amount, add 1.0 to the interest rate of 2 percent (represented as 0.02) to obtain 1.02. Next, raise 1.02 to the 10th power to obtain 1.21899. Subtract 1.0 to obtain 0.21899, and divide by the interest rate of 2 percent (0.02) to obtain 10.9495. Finally, multiply by \$8,000 to obtain the future value of \$87,596.

## Example Two

Assume you make semi-annual payments of \$4,000 for 10 years to an annuity with an annual interest rate of 2 percent. The future value of your annuity is \$88,080. In this example, the interest rate per period is 1.0 percent because there are two payment periods each year, and the total number of payments is 20. To calculate the future value, add 1.0 to the interest rate per period of 1 percent (represented as 0.01) to obtain 1.01. Raise this value to the 20th power to obtain 1.2202, and subtract 1.0 to obtain 0.2202. Divide by the interest rate per period of 1 percent (0.01) to obtain 22.02, and multiply by the payment of \$4,000 to obtain the future value of \$88,080.

## Compounding Interest

As you can see by comparing the two examples, the number of payments you make each year affects the future value of your annuity. When you agree to an annuity with more payments per year, your interest compounds more frequently and the future value of your annuity increases.

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