# How to Calculate a Payoff vs. an Annuity

by Ryan Menezes

When a policy offers you a payment, you often have the chance to choose between an annuity and a lump-sum payoff. The total sum from the annuity will often exceed the payoff's size. This implies a trade-off between the payment's size and the speed at which you'll receive it. But the actual choice is more complicated. Because of inflation, money you receive later is worth less than money you receive now. The sum of the annuity's payments therefore exceeds the total payment's actual current value.

1. Add 1 to the annuity's discount rate, which is the same as the U.S. Treasury borrowing rate. For example, if this rate is 2 percent then calculate 1 + 0.02 = 1.02.

2. Raise this value to the power of the number of years until each payment. For example, if the annuity pays out over the course of 10 years: 1.02^0 = 1; 1.02^1 = 1.02; 1.02^2 = 1.04; 1.02^3 = 1.06; 1.02^4 = 1.08; 1.02^5 = 1.10; 1.02^6 = 1.13; 1.02^7 = 1.15; 1.02^8 = 1.17; 1.02^9 = 1.20.

3. Divide the annuity's payment by each of these values. For example, if the annuity offers 10 equal payments of \$15,000: \$15,000 ÷ 1 = \$15,000; \$15,000 ÷ 1.02 = \$14,705.88; \$15,000 ÷ 1.04 = \$14,423.07; \$15,000 ÷ 1.06 = \$14,150.94; \$15,000 ÷ 1.08 = \$13,888.89; \$15,000 ÷ 1.10 = \$13,636.36; \$15,000 ÷ 1.13 = \$13,274.34; \$15,000 ÷ 1.15 = \$13,043.48; \$15,000 ÷ 1.17 = \$12,820.51; \$15,000 ÷ 1.20 = \$12,500.

4. Add these answers together: \$15,000 + \$14,705.88 + \$14,423.07 + \$14,150.94 + \$13,888.89 + \$13,636.36 + \$13,274.34 + \$13,043.48 + \$12,820.51 + \$12,500 = \$137,443.47. This is the current value of the annuity's total worth.

5. Compare this value to that of the payoff. For example, if the payoff offers \$140,000, it is worth more than the annuity that pays \$150,000 over 10 years.

#### About the Author

Ryan Menezes is a professional writer and blogger. He has a Bachelor of Science in journalism from Boston University and has written for the American Civil Liberties Union, the marketing firm InSegment and the project management service Assembla. He is also a member of Mensa and the American Parliamentary Debate Association.

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