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 an Acquisition Premium?

An acquisition premium is a figure that’s the difference between the estimated real value of a company and the actual price paid to acquire it. An acquisition premium represents the increased cost of buying a target company during a merger and acquisition (M&A) transaction.

There is no requirement that a company pay a premium for acquiring another company; in fact, depending on the situation, it may even get a discount.

Understanding Acquisition Premiums

In an M&A scenario, the company that pays to acquire another company is known as the acquirer, and the company to be purchased or acquired is referred to as the target firm.

Reasons For Paying An Acquisition Premium

Typically, an acquiring company will pay an acquisition premium to close a deal and ward off competition. An acquisition premium might be paid, too, if the acquirer believes that the synergy created from the acquisition will be greater than the total cost of acquiring the target company. The size of the premium often depends on various factors such as competition within the industry, the presence of other bidders, and the motivations of the buyer and seller.

How Does An Acquisition Premium Work?

When a company decides that it wants to acquire another firm, it will first attempt to estimate the real value of the target company. For example, the enterprise value of Macy’s, using data from its 2017 10-K report, is estimated at $11.81 billion. After the acquiring company determines the real value of its target, it decides how much it is willing to pay on top of the real value so as to present an attractive deal to the target firm, especially if there are other firms that are considering an acquisition.

In the example above an acquirer may decide to pay a 20% premium to buy Macy’s. Thus, the total cost it will propose would be $11.81 billion x 1.2 = $14.17 billion. If this premium offer is accepted, then the acquisition premium value will be $14.17 billion – $11.81 billion = $2.36 billion, or in percentage form, 20%.

Arriving at the Acquisition Premium

You also may use a target company’s share price to arrive at the acquisition premium. For instance, if Macy’s is currently trading at $26 per share, and an acquirer is willing to pay $33 per share for the target company’s outstanding shares, then you may calculate the acquisition premium as ($33 – $26)/$26 = 27%.

Using our price-per-share example, let’s assume that there was no premium offer on the table and the agreed-upon acquisition cost was $26 per share. If the value of the company drops to $16 before the acquisition becomes final, the acquirer will find itself paying a premium of ($26 – $16)/$16 = 62.5%.

Acquisition Premiums in Financial Accounting

In financial accounting, the acquisition premium is known as goodwill—the portion of the purchase price that is higher than the sum of the net fair value of all of the assets purchased in the acquisition and the liabilities assumed in the process. The acquiring company records goodwill as a separate account on its balance sheet.

Goodwill factors in intangible assets like the value of a target company’s brand, solid customer base, good customer relations, healthy employee relations, and any patents or proprietary technology acquired from the target company. An adverse event, such as declining cash flows, economic depression, increased competitive environment and the like can lead to an impairment of goodwill, which occurs when the market value of the target company’s intangible assets drops below its acquisition cost. Any impairment results in a decrease in goodwill on the balance sheet and shows as a loss on the income statement.

An acquirer can purchase a target company for a discount, that is, for less than its fair value. When this occurs, negative goodwill is recognized.