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 Angel Investor?

An angel investor (also known as a private investor, seed investor or angel funder) is a high-net-worth individual who provides financial backing for small startups or entrepreneurs, typically in exchange for ownership equity in the company. Often, angel investors are found among an entrepreneur’s family and friends. The funds that angel investors provide may be a one-time investment to help the business get off the ground or an ongoing injection to support and carry the company through its difficult early stages.

Understanding Angel Investors

Angel investors are individuals who seek to invest at the early stages of startups. These types of investments are risky and usually do not represent more than 10% of the angel investor’s portfolio. Most angel investors have excess funds available and are looking for a higher rate of return than those provided by traditional investment opportunities.

Angel investors provide more favorable terms compared to other lenders, since they usually invest in the entrepreneur starting the business rather than the viability of the business. Angel investors are focused on helping startups take their first steps, rather than the possible profit they may get from the business. Essentially, angel investors are the opposite of venture capitalists.

Angel investors are also called informal investors, angel funders, private investors, seed investors or business angels. These are individuals, normally affluent, who inject capital for startups in exchange for ownership equity or convertible debt. Some angel investors invest through crowdfunding platforms online or build angel investor networks to pool capital together.

Origins of Angel Investors

The term “angel” came from the Broadway theater, when wealthy individuals gave money to propel theatrical productions. The term “angel investor” was first used by the University of New Hampshire’s William Wetzel, founder of the Center for Venture Research. Wetzel completed a study on how entrepreneurs gathered capital.

Who Can Be an Angel Investor?

Angel investors are normally individuals who have gained “accredited investor” status but this isn’t a prerequisite. The Securities and Exchange Commission (SEC) defines an “accredited investor” as one with a net worth of $1M in assets or more (excluding personal residences), or having earned $200k in income for the previous two years, or having a combined income of $300k for married couples. Conversely, being an accredited investor is not synonymous with being an angel investor.

Essentially these individuals both have the finances and desire to provide funding for startups. This is welcomed by cash-hungry startups who find angel investors to be far more appealing than other, more predatory, forms of funding.

Sources of Funding

Angel investors typically use their own money, unlike venture capitalists who take care of pooled money from many other investors and place them in a strategically managed fund.

Though angel investors usually represent individuals, the entity that actually provides the funds may be a limited liability company (LLC), a business, a trust or an investment fund, among many other kinds of vehicles.

Investment Profile

Angel investors who seed startups that fail during their early stages lose their investments completely. This is why professional angel investors look for opportunities for a defined exit strategy, acquisitions or initial public offerings (IPOs).

The effective internal rate of return for a successful portfolio for angel investors is approximately 22%. Though this may look good for investors and seem too expensive for entrepreneurs with early-stage businesses, cheaper sources of financing such as banks are not usually available for such business ventures. This makes angel investments perfect for entrepreneurs who are still financially struggling during the startup phase of their business.

Angel investing has grown over the past few decades as the lure of profitability has allowed it to become a primary source of funding for many startups. This, in turn, has fostered innovation which translates into economic growth.

What Is the American Stock Exchange (AMEX)?

The American Stock Exchange (AMEX) was once the third-largest stock exchange in the United States, as measured by trading volume. The exchange, at its height, handled about 10% of all securities traded in the U.S.

Today, the AMEX is known as the NYSE American. In 2008, NYSE Euronext acquired the AMEX. In the subsequent years, it also became known as NYSE Amex Equities and NYSE MKT.

Understanding the American Stock Exchange (AMEX)

The AMEX developed a reputation over time as an exchange that introduced and traded new products and asset classes. For example, it launched its options market in 1975. Options are a type of derivative security. They are contracts that grant the holder the right to buy or sell an asset at a set price on or before a certain date, without the obligation to do so. When the AMEX launched its options market, it also distributed educational materials to help educate investors as to the potential benefits and risks.

In 1993, the AMEX introduced the first exchange traded fund (ETF). The ETF, now a popular investment, is a type of security that tracks an index or a basket of assets. They are much like mutual funds but differ in that they trade like stocks on an exchange.

Over time, the AMEX gained the reputation of listing companies that could not meet the strict requirements of the NYSE. Today, a good portion of trading on the NYSE American is in small cap stocks. It operates as a fully electronic exchange.

History of the American Stock Exchange (AMEX)

The AMEX dates back to the late 18th century when the American trading market was still developing. At that time, without a formalized exchange, stockbrokers would meet in coffeehouses and on the street to trade securities. For this reason, the AMEX became known at one time as the New York Curb Exchange.

The traders who originally met in the streets of New York became known as curbstone brokers. They specialized in trading stocks of emerging companies. At the time, many of these emerging businesses were in industries such as railroads, oil, and textiles, while those industries were still getting off the ground.

In the 19th century, this type of curbside trading was informal and quite disorganized. In 1908, the New York Curb Market Agency was established in order to bring rules and regulations to trading practices.

In 1929, the New York Curb Market became the New York Curb Exchange. It had a formalized trading floor and a set of rules and regulations. In the 1950s, more and more emerging businesses began trading their stocks on the New York Curb Exchange. The value of companies listed on the exchange almost doubled between 1950 and 1960, going from $12 billion to $23 billion during that time. The New York Curb Exchange changed its name to the American Stock Exchange in 1953.

Special Considerations

Over the years, the NYSE American has become an attractive listing place for younger, entrepreneurial companies, some of whom are in the early stages of their growth and certainly not as well-known as blue chip companies. Compared to the NYSE and Nasdaq, the NYSE American trades at much smaller volumes.

Because of these factors, there could be concerns that investors would not be able to quickly buy and sell some securities in the market. To ensure market liquidity—which is the ease at which a security can be converted to cash without impacting its market price—the NYSE American offers electronic designated market makers.

Market makers are individuals or firms that are available to buy and sell a particular security as needed throughout the trading session. These designated market makers have quoting obligations for specific NYSE American-listed companies. In return for making a market for a security, market makers earn money through the bid-ask spread and from fees and commissions. So, despite the fact that the NYSE American is a smaller-volume exchange specializing in listing smaller companies, its use of market makers enables it to maintain liquidity and an orderly market.