# Annual Equivalent Rate (AER)

## What it is:

Same as the effective annual interest rate, the** annual equivalent (AER) rate** is the rate of interest an investor earns in a year after accounting for the effects of compounding. The formula for AER is:

(1 + i/n)^{n} - 1

Where:

i = the stated annual interest rate

n = the number of compounding periods in one year

## How it works (Example):

For example, let’s assume you buy a certificate deposit with a 12% stated annual interest rate. If the bank compounds the interest every month (that is, 12 times per year), then using this information and the formula above, the AER on the CD is:

(1 + .12/12)^{12} - 1 = .12683 or 12.683%

Let’s look at it from another angle. Assume you put $1,000 into the 12% CD. Over 12 months, the investment will look like this:

The percentage change from $1,000 to $1,126.83 is ($1,126.83 - $1,000)/$1,000 = .12683 or 12.683%. Even though the bank has advertised a 12% interest rate, your money actually grew by 12.683%.

## Why it Matters:

The AER rate takes compounding into consideration and is thus almost always higher than the stated annual interest rate. It is a useful tool for evaluating the true return on an investment or the true interest rate paid on a loan, though it often does not include one-time charges ("front-end fees").