How to Calculate Lump Sums and Annuities

Lottery winnings may offer a lump sum payment or an extended annuity.
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Certain scenarios (like pensions and lottery jackpots) offer a choice between a single lump-sum payment and an annuity that pays a series of regular payments. The difficulty in comparing these two options lies with the payment schedule. Future payments made from an annuity are devalued by inflation and not directly comparable to a lump sum payment made today. To properly compare the two options, the total amount received from the annuity should be converted to present value.

Step 1

Research the details of the lump sum payment and the annuity. As an example, on March 30, 2012, a winner of the Mega Millions jackpot would have chosen between a lump sum payment of $359.4 million and an annuity with 26 annual payments of $19.3 million. An interest rate for comparing the two options is also required. Although this can be the expected rate of return of an alternative investment, in which you plan to place your lump sum winnings, you might use the 3.1 percent average annual rate of inflation; using this figure discounts annuity payments by the reduced buying power they have in the future.

Step 2

Add 1 to the interest rate in decimal format. In the example, 1 plus 0.031 gives you 1.031.

Step 3

Raise this figure to the nth power, where "n" is the number of payments expressed as a negative number. Continuing with the example, raise 1.031 to the power of -26 to get 0.4521.

Step 4

Subtract this figure from 1. In the example, 1 minus 0.4521 leaves you with 0.5479.

Step 5

Divide the result by the interest rate. In the example, 0.5479 divided by 0.031 gives you 17.67.

Step 6

Multiply this result times the payment amount to calculate the present value of the annuity. In the example, 17.67 times 19.3 million gives you a present value of 341 million.

Step 7

Compare the lump sum payment to the present value of the annuity. In the example, the $359.4 million lump sum payment is significantly more than the $341 million present value of the annuity. Based on the return, you should take the lump sum payment.

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