# Annual Equivalent Rate (AER) Definition

### What is the equivalent annual rate (ARE)?

The equivalent annual rate (ARE) is the interest rate for a savings account or an investment product that has more than one compounding period. In other words, it is calculated assuming that any interest paid is included in the principal payment balance and the next interest payment will be based on the slightly larger account balance.

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

### The formula for the annual equivalent rate (ARE) is

The

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 declared interest rate} \ end {aligned}

TheAnnual equivalent rate=(1+notrThe)not1or:not=The number of compounding periods (times per year interest is paid)r=The declared interest rateTheThe

### How to calculate the annual equivalent rate (ARE)

To calculate the equivalent annual rate (ARE):

1. Divide the gross interest rate by the number of times per year that interest is paid and add one.
2. Increase the result to the number of times per year that interest is paid.
3. Subtract one from the following result.

The AER is displayed as a percentage (%).

### What does the annual equivalent rate (ARE) tell you?

The equivalent annual rate (ARE) is the real interest rate that an investor will earn for an investment, loan or other product based on the composition. The AER tells investors what they can expect from a return on investment, that is, the actual composition-based investment return, which is higher than the declared or nominal interest rate.

Assuming that interest is calculated (or compounded) more than once a year, the AER will be higher than the interest rate indicated. The more the periods are composed, the greater the difference between the two. The equivalent annual rate (ARE) is also called the effective annual interest rate or annual percentage return (APY).

### Key points to remember

• The equivalent annual rate (ARE) is the rate that an investor can expect to receive from an investment after taking into account the composition.
• The AER is also known as the annual effective rate (EAR) or the annual percentage return (APY).
• The AER will be higher than the declared or nominal rate if there is more than one composition period per year. The gap between the two will increase with periods of composition.

### Example of using the annual equivalent rate (ARE)

Suppose an investor wants to sell all of the securities in his investment portfolio and place all of the products in a savings account. The investor decides between placing the product in bank A, bank B or bank C, depending on the highest rate offered. Bank A has an interest rate of 3.7% which pays interest on an annual basis. Bank B has a listed interest rate of 3.65% which pays interest quarterly and Bank C has a listed interest rate of 3.7% which pays interest semi-annually.

Therefore, bank A would have an equivalent annual rate of 3.7%, or (1 + (0.037 / 1))1 – 1. Bank B has an ARE of 3.7% = (1 + (0.0365 / 4))4 – 1, which is equivalent to that of bank A even if bank B is composed quarterly. Therefore, the investor would be indifferent between placing his money in bank A or bank B.

In contrast, bank C has the same interest rate as bank A, but bank C pays interest semi-annually. Consequently, bank C has an ARE of 3.73%, which is more attractive than the other two banks. The calculation is (1 + (0.037 / 2))2 – 1 = 3.73%.

Now consider a bond issued by General Electric. Since March 2019, General Electric has offered a non-refundable semi-annual coupon with a coupon rate of 4% expiring December 15, 2023. The nominal or declared rate of the bond is 8% – or the coupon rate of 4% multiplied by two coupons. However, the equivalent annual rate is higher since interest is paid twice a year. The ARE of the bond is calculated as (1+ (0.04 / 2))2 -1 = 8.16%.

### The difference between AER and declared interest

Although the interest rate indicated does not take account of the composition, the AER does. The rate indicated will generally be lower than the ARE if there is more than one composition period. The AER is used to determine which banks offer better rates and which investments could be attractive. Learn more about the difference between the ARE and the rate indicated.

### Limits on the use of the annual equivalent rate (ARE)

The equivalent annual rate (ARE) is generally not indicated and must be calculated. In addition, AER does not include any fees that may be related to the purchase or sale of the investment. There is also the fact that the composition itself has its limits, the maximum possible rate being continuous composition.