EAR Calculator

How to Calculate Effective Annual Rate (EAR)

The Effective Annual Rate (EAR) is a crucial concept in finance that helps investors and borrowers understand the true annual cost or return on an investment or loan when compounding is taken into account. This calculator assists you in determining the EAR based on the nominal rate and compounding frequency.

Effective Annual Rate (EAR) Formula

The formula for calculating the Effective Annual Rate is:

$$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$

Where:

• EAR = Effective Annual Rate
• r = Nominal annual interest rate (in decimal form)
• n = Number of compounding periods per year

Calculation Steps

1. Convert the nominal annual rate to decimal form by dividing by 100.
2. Divide the decimal form of the nominal rate by the number of compounding periods per year.
3. Add 1 to the result from step 2.
4. Raise the result from step 3 to the power of the number of compounding periods per year.
5. Subtract 1 from the result in step 4.
6. Multiply the result by 100 to convert it to a percentage.

Example Calculation

Let's calculate the Effective Annual Rate (EAR) for an investment with the following terms:

• Nominal Annual Rate = 6%
• Compounding Frequency = Quarterly (4 times per year)

Step 1: Convert nominal rate to decimal

r = 6% ÷ 100 = 0.06

Step 2: Apply the formula

$$EAR = \left(1 + \frac{0.06}{4}\right)^4 - 1$$

$$EAR = (1 + 0.015)^4 - 1$$

$$EAR = 1.0614 - 1 = 0.0614$$

Step 3: Convert to percentage

EAR = 0.0614 × 100 = 6.14%

Final Result:

• Effective Annual Rate (EAR): 6.14%

Visual Representation

This diagram illustrates the difference between the Nominal Rate and the Effective Annual Rate (EAR). The blue bar represents the Nominal Rate of 6%, while the green bar shows the calculated EAR of 6.14%. This visual comparison helps to understand how compounding affects the actual annual return or cost.