Annual Equivalent Rate (AER)Defined along with Formula & How to Calculate

Written By:
Adiste Mae

What is the Annual Equivalent Rate (AER)?

The Annual Equivalent Rate (AER) is the interest rate that reflects what should actually be paid or earned after the effects of compounding are taken into account in order to normalize the interest rate.

Whenever compounding is present, the AER will always be higher than the nominal or stated interest rate. 

The interest, depending on the payment frequency of interest payments, can be compounded several times in a year through the AER method. 

The other terms used to refer to the AER are the effective annual interest rate or the APY (Annual Percentage Yield). 

When finding out the true Return on Investments (ROI) from interest-bearing assets, the use of AER is highly crucial.

It is the actual interest rate earned by investors for a loan or an investment, based on compounding.

When there is compounding of interest for more than once in a year, the AER is higher than the stated interest rate – and the longer the compounding, the greater is the difference between the two rates. 

Formula for the AER

The following formula is used to compute for the AER:

Annual Equivalent Rate = ( 1 + (r / n) ) n – 1

AER Examples

For a Savings Account

Suppose a person plans to put his savings in a bank but is not sure which one because all three have different offers:

Bank 1 offers an interest rate of 4% that pays quarterly, Bank 2 quoted an interest rate of 3.9% that pays semi-annually, and Bank 3 offers an interest rate of 4.1% that pays annually. 

To know the actual rate earned without taking into account the compounding of interest, the AER for the three banks will be computed as follows:

Bank 1 = 4.06%  (1 + (0.04 / 4)) 4 – 1

Bank 2 = 3.94%  (1 + (0.039 / 2)) 2 – 1

Bank 3 = 4.1%    (1 + (0.041 / 1)) 1 – 1

Based on the example above, even if Bank 3 only pays interest annually, it shows that they offer a more attractive Annual Equivalent Rate (AER) and the investor would receive a higher return if his savings are deposited with Bank 3. 

With a Bond

Company ABC issues a noncallable quarterly coupon with a 1.5% coupon rate that will expire on Jan 31, 2024.

The nominal rate of the coupon bond is 6% which is equivalent to the coupon rate paid four times (quarterly payment). 

The Annual Equivalent Rate therefore is 6.04% (1 + (0.015 / 4)) 4 -1 multiplied by 4 (quarterly payments).

Even when the stated rate of the bond is at 6%, the AER is higher given that it is paid four times a year. 

Annual Equivalent Rate vs. Stated Interest

AER accounts for compounding whereas the Stated Interest does not. If there is more than one compounding period, the stated interest rate will generally be lower than the AER.

For investors who are looking for the best attractive rates for their investments, the AER is helpful in determining which investments to go for. 

Advantages and Disadvantages of the AER

Advantages

• AER accounts for the real rate of interest, taking into account the effects of compounding. 
• It is a helpful tool for investors to evaluate the real return on investments (ROI) on bonds or loans. 

Disadvantages

• The AER is not always provided when investors are looking at investment opportunities and might have to compute for that themselves. 
• There are limitations to compounding. 
• Account fees incurred from the investment are not usually taken into account. 

Special Considerations

Compounding refers to the computation of the interest on the interest earned, and the AER is a significant tool in its computation.

In compounding, an interest is computed on top of the interest earned and these are then added back to the principal amount.

For investors, compounding benefits them because it maximizes the profit that they earn from their investments. 

For those who are borrowing, they would want the effects of compounding minimized.

As for investors, the preference is always to maximize compounding and earn more on interest.

For this reason, it is helpful for people to understand how AERs work and how they are computed to help them make important investment or borrowing decisions. 

What is a Nominal Interest Rate?

The Nominal Rate is the rate of interest that is stated in the loan agreement, not considering any fees or interest compounding.

When the adjustment for the compounding of interest has been made on a loan, it is already referred to as the effective interest rate. 

What is a Real Interest Rate?

In simple terms, the Real Interest Rate is simply the difference between the nominal interest rate and inflation rate.

It reflects the return on investment (ROI) for investors and the real cost of funds for borrowers.

The Real Interest Rate, therefore, is the interest rate adjusted from removing the effects of inflation.