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Future value of an ordinary annuity

N equal payments occur at times 1 through N and the value is at time N.

Read the formula and variables

FVN=C(1+r)N−1rFV_N=C\frac{(1+r)^N-1}{r}

N equal payments occur at times 1 through N and the value is at time N.

Variables and conventions
InputMeaning
CEqual payment
rRate per payment period
NPayment count and final value date

Check a stated example

Five end-period payments of 1,000 at 6% have time-5 FV approximately 5,637.093.

The amounts in the example are synthetic. Keep the original precision through the calculation and round only the displayed result.

Check the domain and timing

The final payment receives no growth period before time N. At zero rate, FV is NC.

A changed date, payment pattern or quotation convention can require a different expression even when the numbers look similar. Identify those features before calculating.

Further references