The formula to calculate the effective annual interest rate (EAR) is:
\[ i = \left(1 + \frac{r}{m}\right)^m - 1 \]
Where:
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.
Let's assume the following values:
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%.
