Formula for the amount of an annuity

An annuity is a fixed sum of money paid at regular intervals.

Amount of an annuity:

P = sum deposited at the end of each year (beginning one year from when the annuity "starts")

r = the interest rate, as a decimal (5%, for example, is r = 0.05)

n = number of years the annuity has run

N = total amount accumulated at the end of n years.

N = (P/r)( (1 + r)ⁿ - 1)

So if $5000 is deposited yearly for 20 years at 5%,

N = (5000/0.05)( (1 + 0.05)²⁰ -1) = 100,000(2.6533 -1) = $165,330

See also the formula for the present value of an annuity