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Effective Annual Rate Calculator

Formula

The formula to calculate the effective annual interest rate (EAR) is:

$i = \left(1 + \frac{r}{m}\right)^m - 1$

Where:

$i$ is the effective annual rate (EAR)
$r$ is the nominal annual interest rate (%)
$m$ is the number of compounding periods per year

What is EAR?

EAR stands for the effective annual rate. EAR is used to describe interest on a loan or mortgage in terms of compounding annual interest rates. In other words, it converts the nominal interest rate to a compounding interest rate.

Example Calculation

Let's assume the following values:

Nominal Annual Interest Rate (r): 5%
Number of Compounding Periods per Year (m): 12

Step 1: Convert the nominal annual interest rate to a decimal:

$r = \frac{5}{100} = 0.05$

Step 2: Calculate the Effective Annual Rate (EAR):

$i = \left(1 + \frac{0.05}{12}\right)^{12} - 1 \approx 0.05116$

Step 3: Convert the result to a percentage:

$EAR = 0.05116 \times 100 \approx 5.116\%$

The effective annual rate is approximately 5.116%.