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Payment for a fully amortizing level-payment model

P is the initial principal and N equal end-period payments repay it under a constant rate with no fees.

Read the formula and variables

C=Pr1−(1+r)−NC=P\frac{r}{1-(1+r)^{-N}}

P is the initial principal and N equal end-period payments repay it under a constant rate with no fees.

Variables and conventions
InputMeaning
PInitial principal
rRate per payment period
NNumber of payments

Check a stated example

Principal 2,000 at 6% for 13 annual payments gives approximately 225.92021068 per payment.

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 zero rate, C = P/N. Rounding each actual payment can require a final adjustment; the formula’s unrounded schedule ends at zero.

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