# Equivalent Interest Rate Calculator

 Interest Rate per Period (R) % Compounding per Period (m) New Compounding per Period (q) Answer: I = 4.0133%R (nominal) = 4%R (effective) = 4.0742% rate per period m = 0.3333%I (nominal) = 4.0133%I (effective) = 4.0742% rate per period q = 1.0033%

## Calculator Use

Convert an interest rate from one compounding frequency to another.

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

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

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%

$i\,=\,4\times\left[\left(1+\frac{0.04}{12}\right)^{12/4}-1\right]\,=\,0.040133$

The effective annual interest rate remains the same.

Cite this content, page or calculator as:

Furey, Edward "Equivalent Interest Rate Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.