Effective Interest Rate Calculator

What is the Effective Interest Rate?

The effective interest rate, also known as the annual percentage yield (APY) or effective annual rate (EAR), is the true annual interest rate earned on an investment or paid on a loan as a result of compounding over time. It takes into account the frequency of compounding and provides a more accurate representation of the actual return or cost compared to the nominal (stated) interest rate.

The Effective Interest Rate Formula

The formula for calculating the effective interest rate is:

\[r_e = (1 + \frac{r}{n})^n - 1\]

Where:

• \(r_e\) = Effective interest rate
• \(r\) = Nominal interest rate (as a decimal)
• \(n\) = Number of compounding periods per year

Step-by-Step Effective Interest Rate Calculation

1. Identify the nominal interest rate (r) and convert it to decimal form if necessary.
2. Determine the number of compounding periods per year (n).
3. Divide the nominal rate by the number of compounding periods (r/n).
4. Add 1 to the result from step 3.
5. Raise the result from step 4 to the power of n.
6. Subtract 1 from the result in step 5.
7. Convert the final result to a percentage if desired.

Example Calculation

Let's calculate the effective interest rate for a nominal rate of 6% compounded monthly:

1. \(r = 6\% = 0.06\), \(n = 12\) (monthly compounding)
2. \(r_e = (1 + \frac{0.06}{12})^{12} - 1\)
3. \(r_e = (1 + 0.005)^{12} - 1\)
4. \(r_e = 1.0616778 - 1 = 0.0616778\)
5. \(r_e = 6.16778\%\)

Visual Representation

The blue portion represents the nominal rate (6%), and the green portion represents the additional return due to compounding (0.17%).