## What is the 'Annual Equivalent Rate - AER'

The annual equivalent rate (AER) is interest that is calculated under the assumption that any interest paid is combined with the original balance and the next interest payment will be based on the slightly higher account balance. Overall, this means that interest can be compounded several times in a year depending on the number of times that interest payments are made.

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## BREAKING DOWN 'Annual Equivalent Rate - AER'

In the United Kingdom, the amount of interest received from savings accounts is listed in AER form.

The AER is calculated as:

Where:
n = number of times a year that interest is paid
r = gross interest rate

The annual equivalent rate uses the same formula to calculate the amount of interest as the annual percentage yield (APY). The AER indicates the amount of interest that has been earned over a specified period. Contrary to the AER, the equivalent annual rate (EAR) is quoted when borrowing money and gives borrowers an idea of the borrowing costs if the borrower remained overdrawn for one year.

## Annual Equivalent Rate Calculation and Interpretation

Similar to the APY, the AER takes into the effects of compounding and measures the amount an account would earn. Moreover, the AER could be used to determine which banks offer better rates and which banks may be attractive investments. Investors should be aware that the annual equivalent rate will typically be higher than the actual annual rate calculated without compounding.

For example, assume an investor wishes to sell all the securities in her investment portfolio and place all her proceeds in a savings account. The investor is deciding between placing her proceeds in either 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 semi-annually.

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%, or ((1 + (0.0365) / 4) ^ 4) - 1, which equivalent to that of bank A even though bank B is compounded quarterly. Therefore, the investor would be indifferent between placing her cash in bank A or bank B. On the other hand, bank C has that same interest rate as bank A, but bank C pays interest semi-annually. Consequently, bank C has an AER of 3.73%, which is more attractive than the other two banks.

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