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Annual Equivalent Rate (AER)

Annual Equivalent Rate (AER)

What Is the Annual Equivalent Rate (AER)?

The annual equivalent rate (AER) is the interest rate for a savings account or investment product that has more than one compounding period. AER is calculated under the assumption that any interest paid is remembered for the principal payment's balance and the next interest payment will be founded on the somewhat higher account balance.

The AER method means that interest can be compounded several times in a year, contingent upon the number of times that interest payments are made.

AER is otherwise called the effective annual interest rate or the annual percentage yield (APY).

The AER is the real interest rate that an investor will earn for an investment, a loan, or another product, in view of compounding. The AER uncovers to investors what they can hope to return from an investment (the ROI) ā€” the genuine return of the investment in view of compounding, which is more than the stated, or nominal, interest rate.

Assuming that interest is calculated ā€” or compounded ā€” at least a time or two per year, the AER will be higher than the stated interest rate. The additional compounding periods, the greater the difference between the two will be.

Formula for the AER

AnnualĀ equivalentĀ rate=(1+rn)nāˆ’1where:n=TheĀ numberĀ ofĀ compoundingĀ periodsĀ (timesĀ perĀ yearĀ interestĀ isĀ paid)r=TheĀ statedĀ interestĀ rate\begin &\text=\left(1 + \frac\right)^n-1\ &\textbf\ &n=\text{The number of compounding periods (times per year interest is paid)}\ &r = \text\ \end

Instructions to Calculate the AER

To compute AER:

  1. Partition the stated interest rate by the number of times a year that interest is paid (compounded) and add one.
  2. Raise the outcome to the number of times a year that interest is paid (compounded)
  3. Deduct one from the subsequent outcome.

The AER is shown as a percentage (%).

Illustration of AER

We should take a gander at AER in the two savings accounts and bonds.

For a Savings Account

Assume an investor wishes to sell every one of the securities in their investment portfolio and place all the proceeds in a savings account. The investor is settling on putting the proceeds in Bank A, Bank B, or Bank C, contingent upon the highest rate offered. Bank A has a quoted interest rate of 3.7% that pays interest on an annual basis. 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 month to month interest might be lower than the rate on an account offering just a single interest payment each year. Be that as it may, when interest is compounded, the former account might offer higher returns than the last option account. For instance, an account offering a rate of 6.25% paid annually may look more appealing than an account paying 6.12% with month to month interest payments. Nonetheless, the AER on the month to month account is 6.29%, instead of an AER of 6.25% on the account with annual interest payments.

In this manner, Bank A would have an annual equivalent rate of 3.7%, or (1 + (0.037/1))1 - 1. Bank B has an AER of 3.7% = (1 + (0.0365/4))4 - 1, which is equivalent to that of Bank An even however Bank B is compounded quarterly. It would hence have no effect on the investor in the event that they placed their cash in Bank An or Bank B.

Then again, Bank C has a similar interest rate as Bank A, yet Bank C pays interest semi-annually. Thus, Bank C has an AER of 3.73%, which is more appealing than the other two banks' AER. The calculation is (1 + (0.037/2))2 - 1 = 3.73%.

With a Bond

We should now consider a bond issued by General Electric. As of March 2019, General Electric offers a noncallable semiannual coupon with a 4% coupon rate terminating Dec. 15, 2023. The nominal, or stated rate, of the bond, is 8% ā€” or the 4% coupon rate times two annual coupons. In any case, the annual equivalent rate is higher, given the way that interest is paid two times every year. The AER of the bond is calculated as (1+ (0.04/2 ))2 - 1 = 8.16%.

Annual Equivalent Rate versus Stated Interest

While the stated interest rate doesn't account for compounding, the AER does. The stated rate will generally be lower than AER on the off chance that there's more than one compounding period. AER is utilized to figure out which banks offer better rates and which investments may be appealing.

Advantages and Disadvantages of the AER

The primary advantage of AER is that it is the real rate of interest since it accounts for the effects of compounding. Also, it is an important instrument for investors since it assists them with assessing bonds, loans, or accounts to grasp their real return on investment (ROI).

Sadly, when investors are assessing different investment options, the AER is normally not stated. Investors must accomplish crafted by computing the actual figure. It's likewise important to keep as a top priority that AER incorporates no fees that may be tied to purchasing or selling the investment. Additionally, compounding itself has limitations, with the maximum conceivable rate being continuous compounding.

Pros of AER

  • Unlike the APR, AER reveals the actual interest rate

  • Crucial in finding the trueĀ ROIĀ from interest-bearing assets.Ā 

Cons of AER

  • Investors must do the work of calculating AER themselves

  • AER doesn't take into account fees that may be incurred from the investment

  • Compounding has limitations, with the maximum possible rate being continuous compounding

## Special Considerations

AER is one of the different ways of computing interest on interest, which is called compounding. Compounding alludes to earning or paying interest on previous interest, which is added to the principal sum of a deposit or loan. Compounding permits investors to support their returns since they can accrue extra profit in light of the interest they've proactively earned.

One of Warren Buffett's well known expressions is, "My wealth has come from a combination of living in America, a few fortunate qualities, and compound interest." Albert Einstein purportedly alluded to compound interest as humanity's most noteworthy development.

At the point when you are borrowing money (as loans), you need to limit the effects of compounding. Then again, all investors need to expand compounding on their investments. Numerous financial establishments will statement interest rates that utilization compounding principles to their advantage. As a consumer, it is important to figure out AER so you can decide the interest rate you are really getting.


  • The AER will be higher than the stated or nominal rate in the event that there is more than one compounding period a year.
  • AER is otherwise called the effective annual interest rate or the annual percentage yield (APY).
  • The annual equivalent rate (AER) is the real interest rate an investment, loan, or savings account will yield in the wake of accounting for compounding.


Where Can I Find an AER Calculator Online?

There are numerous sites that offer instruments for computing AER, including the sites Calculator Soup, Get Calc, and Omni Calculator.

What Is a Nominal Interest Rate?

The nominal interest rate is the advertised or stated interest rate on a loan, without considering any fees or compounding of interest. The nominal interest rate is determined in the loan contract, without adjusting for compounding. When the compounding adjustment has been made, this is the effective interest rate.

What Is a Real Interest Rate?

A real interest rate is an interest rate that has been adjusted to eliminate the effects of inflation. Real interest rates mirror the real cost of funds, on account of a loan (and a borrower) and the real yield (or ROI) for an investor. The real interest rate of an investment is calculated as the difference between the nominal interest rate and the inflation rate.