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Present value of an ordinary annuity

N equal payments occur at times 1 through N, valued at time zero.

Read the formula and variables

PV=C1−(1+r)−NrPV=C\frac{1-(1+r)^{-N}}{r}

N equal payments occur at times 1 through N, valued at time zero.

Variables and conventions
InputMeaning
CEqual payment
rRate per payment period
NPositive payment count

Check a stated example

Five end-period payments of 1,000 at 6% have PV approximately 4,212.3638.

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

At r = 0, use the limit NC rather than dividing by zero. Payment dates are part of the formula’s conditions.

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