# How to Calculate the Present Value of an Annual Annuity

An annuity is a stream of equal payments at fixed intervals for a set time period. You might come across annuities in your everyday life without knowing it. An annual annuity makes these payments every year. Examples of annuities include annual payments from lottery winnings and investments offered by insurance companies that make equal annual payments. You can calculate an annual annuity’s present value to determine how much the stream of payments is worth in today’s dollars based on the annuity’s interest rate. The present value is the lump sum you’d need to pay or deposit now to generate the stream of payments.

Add the annuity’s annual interest rate as a decimal to 1. For example, assume an annuity has an 8 percent annual interest rate. Add 0.08 to 1 to get 1.08.

Raise your result to the exponent -N, in which N represents the number of annual payments the annual makes. In this example, assume the annuity pays for 20 years. Raise 1.08 to the -20th power to get 0.21455.

Subtract your result from 1. In this example, subtract 0.21455 from 1 to get 0.78545.

Divide your result by the annual interest rate as a decimal. In this example, divide 0.78545 by 0.08 to get 9.81813.

Multiply your result by the annuity’s annual payment to calculate the present value of the annual annuity. Concluding the example, assume the annuity pays \$10,000 annually. Multiply 9.81813 by \$10,000 to get a present value of \$98,181.30.

### Tip

• The above calculation assumes the annuity is an ordinary annuity, which makes annual payments at the end of each year. To get the present value of an annual annuity that pays at the beginning of each year -- called an annuity due -- multiply your Step 5 result by (1 + R), in which R is the annual interest rate. For example, assume the above annuity pays at the beginning of each year. Its present value would be \$98,181.30 times (1 + 0.08), or \$106,035.80.

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