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 included in the principal payment’s balance and the next interest payment will be based on the slightly higher account balance.

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

AER is also known as the effective annual interest rate or the annual percentage yield (APY).

The AER is the actual interest rate that an investor will earn for an investment, a loan, or another product, based on compounding. The AER reveals to investors what they can expect to return from an investment (the ROI)—the actual return of the investment based on compounding, which is more than the stated, or nominal, interest rate.

Assuming that interest is calculated—or compounded—more than once a year, the AER will be higher than the stated interest rate. The more compounding periods, the greater the difference between the two will be.

Formula for the AER


$\begin{aligned} &\text{Annual equivalent rate}=\left(1 + \frac{r}{n}\right)^n-1\\ &\textbf{where:}\\ &n=\text{The number of compounding periods (times per year interest is paid)}\\ &r = \text{The stated interest rate}\\ \end{aligned}$​Annual equivalent rate=(1+nr​)n−1where: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:

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

The AER is displayed as a percentage (%).

Example of AER

Let’s look at AER in both savings accounts and bonds.

For a Savings Account

Assume an investor wishes to sell all the securities in their investment portfolio and place all the proceeds in a savings account. The investor is deciding between placing the proceeds in Bank A, Bank B, or Bank C, depending on 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.

Therefore, 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 A even though Bank B is compounded quarterly. It would thus make no difference to the investor if they placed their cash in Bank A or Bank B.

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

With a Bond

Let’s now consider a bond issued by General Electric. As of March 2019, General Electric offers a noncallable semiannual coupon with a 4% coupon rate expiring Dec. 15, 2023. The nominal, or stated rate, of the bond, is 8%—or the 4% coupon rate times two annual coupons. However, the annual equivalent rate is higher, given the fact that interest is paid twice a year. The AER of the bond is calculated as (1+ (0.04 / 2 ))² – 1 = 8.16%.

Annual Equivalent Rate vs. Stated Interest

While the stated interest rate doesn’t account for compounding, the AER does. The stated rate will generally be lower than AER if there’s more than one compounding period. AER is used to determine which banks offer better rates and which investments might be attractive.

Advantages and Disadvantages of the AER

The primary advantage of AER is that it is the real rate of interest because it accounts for the effects of compounding. In addition, it is an important tool for investors because it helps them evaluate bonds, loans, or accounts to understand their real return on investment (ROI).

Unfortunately, when investors are evaluating different investment options, the AER is usually not stated. Investors must do the work of calculating the figure themselves. It’s also important to keep in mind that AER doesn’t include any fees that might be tied to purchasing or selling the investment. Also, compounding itself has limitations, with the maximum possible rate being continuous compounding.

Special Considerations

AER is one of the various ways to calculate interest on interest, which is called compounding. Compounding refers to earning or paying interest on previous interest, which is added to the principal sum of a deposit or loan. Compounding allows investors to boost their returns because they can accrue additional profit based on the interest they’ve already earned.

One of Warren Buffett’s famous quotes is, “My wealth has come from a combination of living in America, some lucky genes, and compound interest.” Albert Einstein reportedly referred to compound interest as mankind’s greatest invention. 

When you are borrowing money (in the form of loans), you want to minimize the effects of compounding. On the other hand, all investors want to maximize compounding on their investments. Many financial institutions will quote interest rates that use compounding principles to their advantage. As a consumer, it is important to understand AER so you can determine the interest rate you are really getting.

What Is Accrued Interest?

In accounting, accrued interest refers to the amount of interest that has been incurred, as of a specific date, on a loan or other financial obligation but has not yet been paid out. Accrued interest can either be in the form of accrued interest revenue, for the lender, or accrued interest expense, for the borrower.

The term accrued interest also refers to the amount of bond interest that has accumulated since the last time a bond interest payment was made.

Understanding Accrued Interest

Accrued interest is calculated as of the last day of the accounting period. For example, assume interest is payable on the 20th of each month, and the accounting period is the end of each calendar month. The month of April will require an accrual of 10 days of interest, from the 21st to the 30th. It is posted as part of the adjusting journal entries at month-end.

Accrued interest is reported on the income statement as a revenue or expense, depending on whether the company is lending or borrowing. In addition, the portion of revenue or expense yet to be paid or collected is reported on the balance sheet as an asset or liability. Because accrued interest is expected to be received or paid within one year, it is often classified as a current asset or current liability.

Accrual Accounting and Accrued Interest

Accrued interest is a result of accrual accounting, which requires that accounting transactions be recognized and recorded when they occur, regardless of whether payment has been received or expended at that time. The ultimate goal when accruing interest is to ensure that the transaction is accurately recorded in the right period. Accrual accounting differs from cash accounting, which recognizes an event when cash or other forms of consideration trade hands.

The revenue recognition principle and matching principle are both important aspects of accrual accounting, and both are relevant in the concept of accrued interest. The revenue recognition principle states that revenue should be recognized in the period in which it was earned, rather than when payment is received. The matching principle states that expenses should be recorded in the same accounting period as the related revenues.

To illustrate how these principles impact accrued interest, consider a business that takes out a loan to purchase a company vehicle. The company owes the bank interest on the vehicle on the first day of the following month. The company has use of the vehicle for the entire prior month, and is, therefore, able to use the vehicle to conduct business and generate revenue.

At the end of each month, the business will need to record interest that it expects to pay out on the following day. In addition, the bank will be recording accrued interest income for the same one-month period because it anticipates the borrower will be paying it the following day.

Accrued Interest Example – Accounting

Consider the following example. Let us assume there is a $20,000 loan receivable with an interest rate of 7.5%, on which payment has been received for the period through the 20th day of the month. In this scenario, to record the extra amount of interest revenue that was earned from the 21st to the 30th of the month, the calculation would be as follows:

• (7.5% x (10 / 365)) x $20,000 = $41.10

The amount of accrued interest for the party who is receiving payment is a credit to the interest revenue account and a debit to the interest receivable account. The receivable is consequently rolled onto the balance sheet and classified as a short-term asset. The same amount is also classified as revenue on the income statement.

The accrued interest for the party who owes the payment is a credit to the accrued liabilities account and a debit to the interest expense account. The liability is rolled onto the balance sheet as a short-term liability, while the interest expense is presented on the income statement.

Both cases are posted as reversing entries, meaning that they are subsequently reversed on the first day of the following month. This ensures that when the cash transaction occurs in the following month, the net effect is only the portion of the revenue or expense that was earned or incurred in the current period stays in the current period.

Using the example above, $123.29 (7.5% x (30/365) x $20,000) is received by the lending company on the 20th day of the second month. Of that, $41.10 related to the prior month and was booked as an adjusting journal entry at the prior month end to recognize the revenue in the month it was earned. Because the adjusting journal entry reverses in the second month, the net effect is that $82.19 ($123.29 – $41.10) of the payment is recognized in the second month. That is equivalent to the 20 days worth of interest in the second month.

Accrued Interest Example – Bonds

Accrued interest is an important consideration when purchasing or selling a bond. Bonds offer the owner compensation for the money they have lent, in the form of regular interest payments. These interest payments, also referred to as coupons, are generally paid semiannually.

If a bond is bought or sold at a time other than those two dates each year, the purchaser will have to tack onto the sales amount any interest accrued since the previous interest payment. The new owner will receive a full 1/2 year interest payment at the next payment date. Therefore, the previous owner must be paid the interest that accrued prior to the sale.

Let’s assume you are interested in buying a bond with a face value of $1,000 and a 5% semiannual coupon. The interest payment is made twice a year on June 1 and December 1 and you plan to buy the bond on September 30. How much accrued interest would you have to pay?

Bond markets use a number of slightly differing day-count conventions to calculate the exact amount of accrued interest. Since most U.S. corporate and municipal bonds use the 30/360 convention, which assumes that each month has 30 days (regardless of the actual number of days in a particular month), we will use that day-count convention in this example.

Step 1: Calculate the exact number of days between the date of the last coupon payment (June 1) and your purchase date (September 30). In this example, the number of days (based on the 30/360 convention) is 120 days.

Step 2: Calculate accrued interest by multiplying the day count by the daily interest rate and face value of the bond.

Thus, accrued interest = 120 x (5% / 360) * $1,000 = $16.67

Step 3: Add the accrued interest to the face value of the bond to get your purchase price.

Purchase price of bond = $1,000 + $16.67 = $1,016.67

On the next coupon payment date (December 1), you will receive $25 in interest. But since you paid $16.67 in accrued interest when you purchased the bond, the net interest received by you is $8.33 ($25 – $16.67), which is precisely the amount of interest you should have received for the 60 days that you owned the bond until the next coupon payment (September 30 to December 1).