# How to Calculate Annuities With Inflation

by C. Taylor

Annuities are retirement vehicles that offer tax-deferred growth while issuing a steady stream of annual payments for a set number of years. The amount you may withdraw each year to maintain this steady stream can be calculated using the annuity formula. However, to take into account the degrading effect of inflation, you need to replace the nominal interest rate with the real interest rate, modified to include inflation. The resulting withdrawal amount will be in present-day dollars, which you can increase with inflation each year to enjoy the same standard of living.

1. Add 1 to your nominal interest rate offered by the annuity. Divide this figure by 1 plus the inflation rate. Finally, subtract 1 to calculate the real interest rate. As an example, if the annuity offered an 8 percent nominal rate and inflation was 3.6 percent, you would divide 1.08 by 1.036 and then subtract 1. This gives you a real interest rate of 0.0425, or 4.25 percent.

2. Add 1 to the real interest rate and raise that figure to the nth power, where n is the number of years before the annuity should reach a zero balance. As an example, if you wanted a 20-year annuity, you would raise 1.0425 to the power of 20 to get 2.299.

3. Divide 1 by the number from the preceding step. In the example, you would have 0.435.

4. Subtract this amount from 1. In the example, you would have 0.565.

5. Divide the amount you invested in the annuity by this amount. In the example, if you invested \$500,000, you would get \$884,955.75.

6. Multiply this figure by the real interest rate. This gives you the withdrawal amount in current dollars. In the example, you would multiply \$884,955.75 by 0.0425. This means you can withdraw the equivalent present-day amount of \$37,610.62.

7. Add 1 to the inflation rate, raise it to the annuity's period number and multiply this number times the withdrawal amount. In the example, to calculate the amount you can withdraw in the third year, you would raise 1.036 to the power of 3 and multiply this by \$37,610.62. This gives you \$41,820.55, which offers the same buying power as \$37,610.62 did during the annuity creation year.

### Items you will need

• Business or scientific calculator

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