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Annual Equivalent Rate (AER)

The rate of interest after taking into account the effects of compounding to normalize the interest rate

What is the Annual Equivalent Rate (AER)?

The Annual Equivalent Rate (AER) is the rate of interest after taking into account the effects of compounding to normalize the interest rate. The AER is the actual interest rate an investment, loan, or savings account will yield after accounting for compounding.

 

Annual Equivalent Rate

 

Summary

  • The Annual Equivalent Rate (AER) is the real rate of interest because it accounts for the effects of compounding.
  • It is an important tool for evaluating bonds, loans, or accounts to understand the real return on investment (ROI) or interest rate.
  • The AER will always be higher than the nominal, or the stated rate, when compounding is present.

 

Annual Equivalent Rate Formula

The formula for the annual equivalent rate is given below:

 

Annual Equivalent Rate - Formula

 

 

How AER is Used

The annual equivalent rate is used to compare the interest rates between loans or investments with different compounding periods, such as weekly, monthly, half-yearly, or yearly. Therefore, it can be used by both an individual looking for the best savings account or an investor comparing bond yields.

 

Significance of the AER

The AER is crucial in finding the true return on investment (ROI) from interest-bearing assets. The nominal rate, or the stated rate, can be materially different than the AER due to the effects of compounding. It means that the AER is always higher than the nominal rate when considering compounding.

The table below visualizes the potential differences in the annual equivalent rate and the nominal rate with different compounding frequencies:

 

Annual Equivalent Rates of Different Compounding Frequencies
Nominal Interest RateSemi-AnnuallyQuarterlyMonthlyWeeklyDaily
1%1.0025%1.0038%1.0046%1.0049%1.0050%
2%2.0100%2.0151%2.0184%2.0197%2.0201%
3%3.0225%3.0339%3.0416%3.0446%3.0453%
4%4.0400%4.0604%4.0742%4.0795%4.0808%
5%5.0625%5.0945%5.1162%5.1246%5.1267%
6%6.0900%6.1364%6.1678%6.1800%6.1831%
7%7.1225%7.1859%7.2290%7.2458%7.2501%
8%8.1600%8.2432%8.3000%8.3220%8.3278%
9%9.2025%9.3083%9.3807%9.4089%9.4162%
10%10.2500%10.3813%10.4713%10.5065%10.5156%
15%15.5625%15.8650%16.0755%16.1583%16.1798%
20%21.0000%21.5506%21.9391%22.0934%22.1336%
25%26.5625%27.4429%28.0732%28.3256%28.3916%

 

Annual Equivalent Rate vs. Nominal Interest – Example

For example, let’s say Bond A offers a semi-annual coupon rate of 3%. The nominal rate of the bond is 6% since it is two 3% coupons. However, the AER of the bond will be higher given that interest is paid out two times a year. Therefore, the AER of the bond will be calculated as:

AER = (1+ (0.06 / 2 )^2)) – 1 = 6.09%

 

Bond B, on the other hand, offers a quarterly coupon rate of 1.5%. The nominal rate of the bond is still 6%. However, the AER will be even higher, as the coupons are paid out four times a year. Therefore, the AER of the bond will be:

AER = (1+ (0.06/4)^4)) – 1 = 6.14%

 

After analyzing the AER of the two bond options, a rational investor will select Bond B, assuming all else equal, even though both bonds are the same from face value.

 

Related Readings

CFI is the official provider of the global Certified Banking & Credit Analyst (CBCA)™ certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional CFI resources below will be useful:

  • Continuously Compounded Return
  • Rate of Return
  • Simple Interest vs Compounded Interest
  • Investing: A Beginner’s Guide

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