Effective Annual Rate (EAR) Calculator
Effective Annual Rate (EAR)
Understanding the Effective Annual Rate of Return
The Effective Annual Rate (EAR) represents the actual return on an investment or the true cost of a loan when compounding occurs more than once a year. While financial institutions often advertise a "nominal" or "stated" rate, the EAR accounts for the "interest on interest" that accumulates during the year.
The EAR Formula
To calculate the effective annual rate of return, we use the following mathematical formula:
Where:
- i = The nominal annual interest rate (expressed as a decimal).
- n = The number of compounding periods per year.
Why the Effective Rate is Higher Than the Nominal Rate
As the frequency of compounding increases, the effective annual rate also increases. This is because the interest earned in the first period is added to the principal, and in the second period, you earn interest on that new, larger amount. For example, if you have a 10% nominal rate compounded monthly, you aren't just getting 10% at the end of the year; you are getting 0.833% every month, which compounds upon itself.
Practical Example
Suppose you have a savings account with a 6% nominal annual rate compounded quarterly (4 times a year).
- Convert the rate to a decimal: 0.06
- Divide by periods: 0.06 / 4 = 0.015
- Add 1: 1.015
- Raise to the power of 4: (1.015)4 ≈ 1.06136
- Subtract 1: 0.06136 or 6.136%
In this scenario, the effective annual rate of return is 6.136%, which is 0.136% higher than the stated nominal rate.
When to Use EAR
EAR is the gold standard for comparing different financial products. If one bank offers 5.1% compounded annually and another offers 5.0% compounded daily, the EAR allows you to see which one actually yields more profit at the end of the 12-month cycle.