# Equivalent interest rate

An **equivalent interest rate** is a financially accurate sub-annual interest rate at the nominal annual rate . It is determined by the following formula:{\ displaystyle \ textstyle i_ {e} = (1 + i) ^ {\ frac {1} {n}} – 1}where i _{e} = equivalent interest, i = nominal interest and n the number of sub-annual periods.

The equivalent interest rate should not be confused with the proportional interest rate , which is limited to dividing the nominal rate by the number of sub-annual periods, which is financially non-equivalent.

The equivalent interest rate presupposes a compound interest calculation , by inducing a reinvestment of the sub – annual rate paid.

Example: if you consider a nominal interest rate of 4%, the equivalent quarterly interest rate is {\ displaystyle \ scriptstyle (1 + 4 \%) ^ {\ frac {1} {4}} – 1 = 0.985 \%}.

By way of illustration, a capital of 100 € placed at 4% yields at the end of one year 4 € (100 x 4%). This is equivalent to the capital of € 100 placed at 0.985% quarterly, which also pays after one year € 4: