How to Calculate Annuity Purchase Rates

by C. Taylor

Annuities offer a series of regular, fixed payments from an investment account and continue until the account is depleted. The initial purchase price, or investment total, of the annuity depends on the length of the payout period, the annual payment and the interest rate. Some annuities are purchased long before the payout period begins. To calculate the purchase price of these, you also need to factor in the length of time between the initial investment and the start of the payout period.

1. Add one to the interest rate, in decimal form. For example, if you were offered a 5 percent interest rate, you would get 1.05.

2. Raise this figure to the N power, where N is the number of years of the investment period, converted to a negative number. In the example from the previous step, if wanted to receive 15 annual payments, which begin at retirement, then you would raise 1.05 to the power of -15 to get 0.48102.

3. Subtract this number from 1. In the example, this gives you 0.51898.

4. Divide this number by the interest rate in decimal format (0.05). In the example, you get 10.3797.

5. Multiply this amount by the amount of the annual payments. In the example, if you wanted to receive annual payments of $10,000, you would multiply $10,000 by 10.3797 to get $103,796.58. This represents the required balance at the beginning of the payout period to achieve 15 annual payments of $10,000. However, if you purchase the annuity years earlier and allow that investment to compound until the payout period begins, then your investment will be less.

6. Add 1 to the interest rate and raise this figure to the number of years between the initial investment and the beginning of the payout period. In the example, if you are 30 years old and want to receive payments at 65, then you would raise 1.05 to the power of 35 to get 5.51601.

7. Divide the required annuity balance at the beginning of the payout period this figure from Step 6, which in the example would be $103,796.58 by 5.51601 to get $18,817.31. Therefore, to receive 15 annual payments of $10,000, starting 35 years from now, you would need to purchase an $18,817.31 annuity.

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