Equivalent Interest Rate Calculator

Calculator Use

Convert a nominal interest rate from one compounding frequency to another while keeping the effective interest rate constant.

Given the periodic nominal rate r compounded m times per per period, the equivalent periodic nominal rate i compounded q times per period is

\( i = q\times\left[\left(1+\dfrac{r}{m}\right)^\frac{m}{q}-1\right] \)

where r = R/100 and i = I/100.

For example, you have a loan at an annual rate of 4% that compounds monthly (m=12) however your payments are made quarterly (q=4) so your interest will be calculated quarterly.  What is the equivalent annual rate that coincides with quarterly compounding? 4.0133%

\( i = 4\times\left[\left(1+\dfrac{0.04}{12}\right)^\frac{12}{4}-1\right] \)

\( i = 0.040133 \)

The effective annual interest rate remains the same.

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