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formula for the present value of an annuity

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

Present value of an annuity:



P = the amount that needs to be invested now to give an annuity paying N at the end of each year for n years, beginning in one year. Assumes that money not yet paid out earns interest at...

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

P = (N/r)( 1 - (1 + r)-n )

For example, if the plan is to get paid $20,000 a year for 20 years and do it with an annuity when the interest rate is 5%, the amount you'd need to invest in the annuity is

P = (20000/0.05)( 1 - (1 + 0.05)-20 ) = 400000(1 - .37689) = $249,244

See also the formula for the amount of an annuity