# How to Find the IRR of an Annuity

An investment's internal rate of return, or IRR, can give you an idea of the investment's profitability. In general, the higher the internal rate of return, the better, and a "good" investment is one in which the IRR is higher than the return you could get from doing something else with your money. If the investment is an annuity, you can find the IRR yourself by applying a formula.

## IRR Defined

Financial professionals refer to the internal rate of return of an investment as the interest rate that makes the net present value of all cash flows equal to zero. In more basic terms, it's the effective interest rate you would be earning if you assume that the money you eventually get out of the investment is equal in value, in today's dollars, to the money you put into it.

## Annuities

An annuity is any series of equal payments distributed at regular intervals. The interest you earn on bonds is an annuity, for example, as are defined benefit pension payments. Installment loans such as mortgages and car loans are also annuities, although in those cases, you're the one making the payments rather than receiving them. When you purchase an annuity, you pay a certain amount of money in advance, then receive payments later. The upfront payment is a negative cash flow for you, and the payments are positive cash flows.

## Formula

The formula for calculating the present value of an annuity -- that is, the value in current dollars of the future annuity payments -- is as follows: PV = PMT * [(1-(1+r)^-n)/r] In the formula, "PV" stands for present value; "PMT" is the value of each payment you receive; "r" is the interest rate per period between payments; and "n" is the number of periods in the annuity. When calculating internal rate of return, you're looking for the value for "r" that makes the present value ("PV") of the annuity equal to the amount of money you paid for the annuity.

## Example

Say you paid \$200,000 for an annuity that, starting one year from today, will pay you \$20,000 a year for the next 30 years. To get the IRR, you need an annual interest rate that satisfies this equation: \$200,000 = \$20,000 * [(1-(1+r)^-30)/r] If you have a financial calculator, you can compute the value for "r" using the "time value of money" functions. Set present value to -\$200,000 (negative because it's a negative cash flow to you), set payment to \$20,000, and set the number of periods to 30. Spreadsheet programs such as Microsoft Excel also calculate internal rate of return using a function usually called "IRR." Supply information about the present value and the payments, and the program will calculate IRR. In this case, the IRR is about 9.31 percent.