The Annual Equivalent Rate (AER) is used to compare savings and investment products that may pay interest at different rates or with different compounding periods. AER shows the true yearly interest rate, taking compound interest into account.

Financial products often advertise interest paid monthly, quarterly or annually. Comparing these rates directly can be misleading because interest paid more frequently earns interest on interest. AER converts all rates to a common annual basis, making comparisons fair.

If interest is paid once per year, the AER is the same as the stated annual rate. If interest is paid more frequently, the AER will be higher than the stated rate because of compounding.

AER is calculated using a multiplier. If an interest rate of \( r \) is paid \( n \) times per year, the AER multiplier is:

$$
\left(1 + \frac{r}{n}\right)^n
$$

The AER percentage is then found by subtracting 1 and converting to a percentage.

For example, suppose a savings account pays \( 4\% \) interest per year, compounded monthly. The monthly rate is:

$$
\frac{0.04}{12}
$$

The AER multiplier is:

$$
\left(1 + \frac{0.04}{12}\right)^{12}
$$

$$
= 1.0407
$$

This corresponds to an AER of \( 4.07\% \).

Now compare this with another account that pays \( 4.05\% \) interest annually. Even though \( 4\% \) sounds lower than \( 4.05\% \), the monthly compounding means the first account has the higher AER and is the better option.

When comparing financial products, always use the AER, not the stated interest rate. AER accounts for how often interest is added and allows you to make accurate comparisons between savings accounts and investments.