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Present value of a level perpetuity

A constant positive payment begins one period from now and r is positive.

Read the formula and variables

PV0=CrPV_0=\frac{C}{r}

A constant positive payment begins one period from now and r is positive.

Variables and conventions
InputMeaning
CEqual payment forever
rPositive discount rate per payment interval

Check a stated example

A constant payment of 4 at 8% per period gives time-zero value 50.

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 positive-rate condition supplies convergence of the infinite discounted stream. A finite-horizon annuity is a different pattern.

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