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Effective rate for a shorter or longer interval

m equal periods together form one year and the annual growth factor is positive.

Read the formula and variables

rperiod=(1+EAR)1/m−1r_{period}=(1+EAR)^{1/m}-1

m equal periods together form one year and the annual growth factor is positive.

Variables and conventions
InputMeaning
EAREffective annual rate
mEqual periods per year
r_periodEffective rate for one of those periods

Check a stated example

At 6% EAR, a monthly effective rate is approximately 0.4867550565%, not 0.5%.

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

Raising the monthly factor to the twelfth power recovers the 1.06 annual factor.

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