EAR Calculator – Find the Effective Annual Rate

Calculate the effective annual rate (EAR) by entering the annual rate and compounding frequency in the calculator below.

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Effective Annual Rate:

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Learn how we calculated this below


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How to Calculate the Effective Annual Rate

The effective annual rate (or EAR) converts a simple interest rate into a compounding interest rate. A compounding interest rate earns interest on a prior period’s interest payments and the principal value. A simple interest rate is one in which interest is earned solely on the original principal value.

Since the EAR is a compounding interest rate, the more times interest is compounded in a year, the higher the interest rate will be. This is the “n” term in the effective annual rate formula below.

If you are a lender, you would want interest to be compounded continuously since that will generate the highest interest for you. However, if you are a borrower, the lowest interest rate would be interest compounded annually.

The different compounding periods in the effective annual rate calculator are continuous, daily, weekly, semimonthly, monthly, quarterly, semiannually, and annually. These are in order of the highest EAR to the lowest.

You can also use our APY calculator to calculate the annual percentage yield, which is essentially the same rate as the EAR.

EAR Formula

The effective annual rate formula is as follows:

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

Where:
EAR = effective annual rate
r = annual rate
n = compounding periods

Example

Let’s use an example to show the difference in the EAR with the same interest rate, but different compounding periods. We will assume an annual rate of 7% and see what the difference is between semimonthly (n = 24) and semiannually (n = 2) compounding.

Semimonthly

EAR = \left ( 1 + \frac{0.07}{24} \right )^{24} − 1
EAR = \left ( 1 + 0.00291667 \right )^{24} − 1
EAR = 1.072399 − 1
EAR = 7.2399\%

Semiannually

EAR = \left ( 1 + \frac{0.07}{2} \right )^{2} − 1
EAR = \left ( 1 + 0.035 \right )^{2} − 1
EAR = 071225 − 1
EAR = 7.1225\%

You can find the same rates using the effective annual rate calculator above. This shows that compounding the interest rate 24 times per year results in a higher effective annual interest rate than compounding only twice a year.

The range is from 7.0% under annual compounding to 7.2508% under continuous compounding.

What is the Effective Annual Rate Used For?

The effective annual rate can be used in savings accounts, checking accounts, or a certificate of deposit.

Assume you have opened a $10,000 certificate of deposit that pays you 4% compounded quarterly. Instead of receiving 4% interest at the end of the year, the financial institution will pay you 1% each quarter.

The effective annual rate calculator shows that this gives an EAR of 4.0604%. Instead of $400 in interest, you will have $406.04. This extra $6 might seem insignificant, but with larger amounts and a longer period, compounding interest will lead to a much larger amount.

This extra interest is free. There is no extra work or risk involved in receiving it.

Although a compounding rate can be found on a loan, it is much rarer. When you are making loan payments each month, you are not paying interest on the prior period’s interest payments. You only pay interest on the current principal value.

Use our APR calculator to calculate the true cost of borrowing on a loan that includes financed and prepaid fees.