# 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

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

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.