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.