Annual Equivalent Rate - AER

The annual equivalent rate is the actual rate of return you get on some investment, taking into account the impact of compounding.

When you invest in something that has a stated interest rate (say, a savings account or a CD) the actual rate of return will tend to be slightly higher than the advertised amount. That's because these investments typically compound the interest at various intervals, usually monthly. Compounding means the interest you earn eventually earns its own interest. This little extra bit adds up over time, and the annual rate often turns out higher than the stated rate.

So say you have $100 in a CD that pays a nominal rate of 6%. The interest is computed on a monthly basis and compounded. In the first month, you will earn $0.50 in interest. (If you don't take our word for it: 6% over the 12 months of the year means in any given month you earn 0.5% in interest...as in 6% divided by 12 equals 0.5% per month. With a $100 initial investment, a 0.5% monthly rate would lead to $0.50 in interest earned in the first month. We're not doing that math for you; get a calculator if you don't believe us.)

So now we're going into month number two. There's $100.50 in the CD. You earn another month's interest at 0.5% per month. But wait, now we're earning that interest on $100.50 rather than $100. So the resulting interest payment is slightly higher.

The interest earned in the second month is $0.5025, or 50 cents plus a quarter of cent extra. Assuming the CD isn't provided by the companies in either Office Space or Superman III, that quarter of a penny is added to your total.

Do this same process over the course of a full year, adding up all those fractions of a cent, and your closing balance for the year would be $105.12. That's 12 cents more than the 5% advertised interest rate. That means your annual equivalent rate is 5.12%.

There's an equation for figuring out annual equivalent rate. It goes like this:

(1 + i/n)n - 1

Here, "i" equals the stated interest rate (5% in the example we gave), while "n" equals the number of compounding periods (in the example, the number of months in the year, or 12).