The annual equivalent rate (AER) is the interest rate for a savings account or investment product with more than one compounding period. AER assumes that any interest paid is included in the principal balance for the next interest payment, leading to a slightly higher account balance over time.
Key Takeaways
- The annual equivalent rate (AER) is the actual interest rate an investment, loan, or savings account yields after accounting for compounding.
- AER is also known as the effective annual interest rate or the annual percentage yield (APY).
- The AER will be higher than the stated or nominal rate if there is more than one compounding period a year.
The AER method means that interest can be compounded several times a year, depending on the number of interest payments made.
Formula for the AER
The AER is calculated using the following formula:
AER = (1 + r/n)^n - 1
where:
- n = The number of compounding periods (times per year interest is paid)
- r = The stated interest rate
How to Calculate the AER
To calculate AER:
- Divide the stated interest rate by the number of times a year that interest is paid (compounded) and add one.
- Raise the result to the number of times a year that interest is paid (compounded).
- Subtract one from the subsequent result.
The AER is displayed as a percentage (%).
Real-Life Examples of AER
For a Savings Account
Assume an investor wishes to sell their entire investment portfolio and place all the proceeds in a savings account. The investor is deciding between Bank A, Bank B, or Bank C, based on the highest rate offered. Bank A has a quoted interest rate of 3.7% that pays interest annually. 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.
The stated interest rate paid on an account offering monthly interest may be lower than one offering annual interest. However, when interest is compounded, the account with more frequent payments may offer higher returns. For example, an account offering a rate of 6.25% paid annually may look more attractive than one offering 6.12% monthly. However, the AER on the monthly account is 6.30%, versus 6.25% on the annual account.
Therefore, Bank A’s AER remains 3.7%, calculated as $(1 + \frac{0.037}{1})^1 - 1$. Bank B’s AER is also calculated $(1 + \frac{0.0365}{4})^4 - 1$, resulting in 3.73%. Bank C, paying semi-annually, offers the most attractive AER of 3.73%, calculated as $(1 + \frac{0.037}{2})^2 - 1$.
With a Bond
Consider a bond issued by General Electric in March 2019, offering a noncallable semiannual coupon with a 4% coupon rate, expiring Dec. 15, 2023. The nominal rate of the bond is 8%, or the 4% coupon rate times two annual coupons. However, the AER for the bond is (1+ $\frac{0.08}{2}$)^2 - 1 = 8.16% due to semiannual payments.
Annual Equivalent Rate vs. Stated Interest
The stated interest rate does not account for compounding, whereas the AER does. AER is generally higher than the stated rate if compounding occurs more than once a year, helping determine which banks or investments might offer better rates.
Advantages and Disadvantages of the AER
Pros of AER:
- Reveals the true interest rate, unlike the APR
- Essential for understanding real ROI from interest-bearing assets
Cons of AER:
- Requires investors to calculate AER themselves
- Doesn’t account for additional fees
- Maximum potential rate is limited by continuous compounding
Special Considerations
AER is a method to calculate interest on interest, called compounding. Compounding refers to earning or paying interest on previously earned or paid interest, added to the principal sum. This allows for greater returns or greater costs, depending on the scenario. Hence, it’s important to understand AER to gauge the actual interest being earned from investments or being paid on loans.
Warren Buffett and Albert Einstein have both extolled the virtues of compounding, emphasizing its power in wealth creation. Understanding AER helps investors align their strategies to maximize benefits from compounding.
The Bottom Line
The annual equivalent rate, or AER, is the true interest rate on a loan or investment after compounding. Higher than the nominal rate if compounded more than once a year, AER gives a better picture of returns, making it crucial for optimizing investment strategies.
Related Terms: Effective Annual Interest Rate, Annual Percentage Yield, Compounding Interest, Savings Accounts, Investment Returns.
References
- The Giving Pledge. “My philanthropic pledge”.
- Inc. “Why Einstein Considered Compound Interest the Most Powerful Force in the Universe”.
