Effective Annual Rate (EAR) Calculator
Understanding the Effective Annual Rate (EAR)
The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or effective interest rate, is the real annual rate of return earned on an investment or paid on a loan. It takes into account the effect of compounding. Compounding is the process where interest is earned not only on the initial principal but also on the accumulated interest from previous periods. This means that if interest is compounded more frequently than once a year, the EAR will be higher than the stated nominal annual interest rate.
Why is EAR Important?
EAR is a crucial metric for comparing different financial products, especially those with varying compounding frequencies. For instance, a savings account offering 5% interest compounded annually will yield less than an account offering 4.8% interest compounded monthly. By converting both to their EAR, you can accurately determine which offers a better return. Similarly, when taking out loans, understanding the EAR helps you grasp the true cost of borrowing.
How to Calculate EAR
The formula to calculate the Effective Annual Rate is:
EAR = (1 + r/n)^n – 1
Where:
- r is the nominal annual interest rate (expressed as a decimal).
- n is the number of compounding periods per year.
In our calculator, we've slightly adjusted the input to directly use the periodic interest rate (which is r/n) for simplicity and to avoid needing the nominal rate separately if it's not readily available. The formula used in the calculator is:
EAR = (1 + Periodic Interest Rate)^Number of Compounding Periods per Year – 1
Example Calculation
Let's say you have an investment with a periodic interest rate of 0.5% per month and interest is compounded monthly. This means:
- Periodic Interest Rate = 0.005 (0.5% as a decimal)
- Number of Compounding Periods per Year = 12
Using the EAR formula:
EAR = (1 + 0.005)^12 – 1
EAR = (1.005)^12 – 1
EAR = 1.06167781 – 1
EAR = 0.06167781
This means the Effective Annual Rate is approximately 6.17%. If the nominal annual rate were simply stated as 6%, this compounded monthly would result in a higher actual return.