 Online Calculators

# Equivalent Interest Rate Calculator

Equivalent Rate Calculator
I = 4.01335%

Rn (nominal) = 4%
Re (effective) = 4.07415%

In (nominal) = 4.01335%
Ie (effective) = 4.07415%

## 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.

Cite this content, page or calculator as:

Furey, Edward "Equivalent Interest Rate Calculator" at https://www.calculatorsoup.com/calculators/financial/equivalent-interest-rate-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: November 15, 2023