## What Is the Annual Equivalent Rate (AER)?

The AER is the interest rate for a savings account or investment product that has more than one compounding period. That is, it's calculated under the assumption that any interest paid is included in the principal payment's balance and the next interest payment will be based on the slightly higher account balance.

### Key Takeaways

- The AER is the rate an investor can expect to earn from an investment after taking compounding into account.
- AER is also known as the effective annual rate (EAR) or the annual percentage yield (APY).
- The AER will be higher than the stated or nominal rate if there is more than one compounding period a year. The spread between the two will grow greater with more compounding periods.

Overall, this means that interest can be compounded several times in a year depending on the number of times that interest payments are made.

## The formula for the AER

$\begin{aligned} &\text{Annual equivalent rate}=\left(1 + \frac{r}{n}\right)^n-1\\ &\textbf{where:}\\ &n=\text{The number of compounding periods (times per year interest is paid)}\\ &r = \text{The stated interest rate}\\ \end{aligned}$

## How to calculate AER

To calculate AER:

- Divide the gross interest rate by the number of times a year that interest is paid and add one.
- Raise the result to the number of times a year that interest is paid.
- Subtract one from the subsequent result.

The AER is displayed as a percentage (%).

## What Does the AER Tell You?

The AER is the actual interest rate that an investor will earn for an investment, a loan, or another product based on compounding. The AER reveals to investors what they can expect to return from an investment, meaning the actual return of the investment based on compounding, which is more than the stated or nominal interest rate.

Assuming interest is calculated (or compounded) more than once a year, the AER will be higher than the stated interest rate. The more compounding periods, the greater the difference between the two will be. The annual equivalent rate (AER) is also known as effective annual interest rate or annual percentage yield (APY).

The annual equivalent rate (AER) is interchangeable with the phrases "effective interest rate (EIR)" and "effective annual interest rate."

## Example of How to Use AER

Let's look at AER in both savings accounts and bonds.

### For a Savings Account

Assume an investor wishes to sell all the securities in their investment portfolio and place all the proceeds in a savings account. The investor is deciding between placing the proceeds in Bank A, Bank B, or Bank C, depending on the highest rate offered. Bank A has a quoted interest rate of 3.7% that pays interest on an annual basis. Bank B has a quoted interest rate of 3.65% that pays interest quarterly, and Bank C has a quoted interest rate of 3.7% that pays interest semiannually.

Therefore, Bank A would have an annual equivalent rate of 3.7%, or (1 + (0.037 / 1))^{1} - 1. Bank B has an AER of 3.7% = (1 + (0.0365 / 4))^{4} - 1, which is equivalent to that of Bank A even though Bank B is compounded quarterly. It would thus make no difference to the investor if they placed their cash in Bank A or Bank B.

On the other hand, Bank C has the same interest rate as Bank A, but Bank C pays interest semiannually. Consequently, Bank C has an AER of 3.73%, which is more attractive than the other two banks' AER. The calculation is (1 + (0.037 / 2))^{2} - 1 = 3.73%.

### With a Bond

Let's now consider a bond issued by General Electric. As of March 2019, General Electric offers a noncallable semiannual coupon with a 4% coupon rate expiring December 15, 2023. The nominal, or stated rate, of the bond is 8%—or the 4% coupon rate times two annual coupons. However, the annual equivalent rate is higher given the fact that interest is paid twice a year. The AER of the bond is calculated as (1+ (0.04 / 2 ))^{2} - 1 = 8.16%.

## The Difference Between AER and Stated Interest

While the stated interest rate doesn't account for compounding, the AER does. The stated rate will generally be lower than AER if there's more than one compounding period. AER is used to determine which banks offer better rates and which investments might be attractive. Learn more about the difference between AER and stated rate.

## Limitations of Using AER

The AER usually isn't stated and must be calculated. As well, AER doesn't include any fees that might be tied to purchasing or selling the investment. There's also the fact that compounding itself has limitations, with the maximum possible rate being continuous compounding.

## Learn More About AER

The AER is one of the various ways to calculate interest on interest—compounding. Compounding allows investors to boost their returns by making money on interest. One of Warren Buffett's famous quotes is, "My wealth has come from a combination of living in America, some lucky genes, and compound interest."