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 Annual General Meeting (AGM)?

An annual general meeting (AGM) is a yearly gathering of a company’s interested shareholders. At an AGM, the directors of the company present an annual report containing information for shareholders about the company’s performance and strategy.

Shareholders with voting rights vote on current issues, such as appointments to the company’s board of directors, executive compensation, dividend payments, and the selection of auditors.

How an Annual General Meeting (AGM) Works

An annual general meeting, or annual shareholder meeting, is primarily held to allow shareholders to vote on both company issues and the selection of the company’s board of directors. In large companies, this meeting is typically the only time during the year when shareholders and executives interact.

The exact rules governing an AGM vary according to jurisdiction. As outlined by many states in their laws of incorporation, both public and private companies must hold AGMs, though the rules tend to be more stringent for publicly traded companies.

Public companies must file annual proxy statements, known as Form DEF 14A, with the Securities and Exchange Commission (SEC). The filing will specify the date, time, and location of the annual meeting, as well as executive compensation and any material matters of the company concerning shareholder voting and nominated directors.

Annual general meetings (AGMs) are important for the transparency they provide, the ability to include shareholders, as well as bringing management to accountability.

Qualifications for an Annual General Meeting (AGM)

The corporate bylaws that govern a company, along with its jurisdiction, memorandum, and articles of association, contain the rules governing an AGM. For example, there are provisions detailing how far in advance shareholders must be notified of where and when an AGM will be held and how to vote by proxy. In most jurisdictions, the following items, by law, must be discussed at an AGM:

• Minutes of the previous meeting: The minutes of the previous year’s AGM must be presented and approved.
• Financial statements: The company presents its annual financial statements to its shareholders for approval.
• Ratification of the director’s actions: The shareholders approve and ratify (or not) the decisions made by the board of directors over the previous year. This often includes the payment of a dividend.
• Election of the board of directors: The shareholders elect the board of directors for the upcoming year.

Additional Topics Covered at an Annual General Meeting (AGM)

If the company has not been performing well, the AGM is also when shareholders can question the board of directors and management as to why performance has been poor. The shareholders can demand satisfactory answers as well as to inquire about the strategies that management plans to implement to turn the company around.

The AGM is also when shareholders can vote on company matters other than electing the board of directors. For example, if management is contemplating a merger or an acquisition, the proposal can be presented to the shareholders and they can vote on whether or not the company should proceed.

Several other elements may be added to an AGM agenda. Often, the company’s directors and executives use an AGM as their opportunity to share their vision of the company’s future with the shareholders. For example, at the AGM for Berkshire Hathaway, Warren Buffett delivers long speeches on his views of the company and the economy as a whole.

Berkshire Hathaway’s annual gathering has become so popular that it is attended by tens of thousands of people each year, and it’s been dubbed the “Woodstock for Capitalists.”

What Is Average Annual Growth Rate (AAGR)?

The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It doesn’t take compounding into account.

Formula for Average Annual Growth Rate (AAGR)

$\begin{aligned} &AAGR = \frac{GR_A + GR_B + \dotso + GR_n}{N} \\ &\textbf{where:}\\ &GR_A=\text{Growth rate in period A}\\ &GR_B=\text{Growth rate in period B}\\ &GR_n=\text{Growth rate in period }n\\ &N=\text{Number of payments}\\ \end{aligned}$​AAGR=NGRA​+GRB​+…+GRn​​where:GRA​=Growth rate in period AGRB​=Growth rate in period BGRn​=Growth rate in period nN=Number of payments​

Understanding the Average Annual Growth Rate (AAGR)

The average annual growth rate helps determine long-term trends. It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed. The ratio tells you your average annual return.

The average annual growth rate is a calculation of the arithmetic mean of a series of growth rates. AAGR can be calculated for any investment, but it will not include any measure of the investment’s overall risk, as measured by its price volatility. Furthermore, the AAGR does not account for periodic compounding.

AAGR is a standard for measuring average returns of investments over several time periods on an annualized basis. You’ll find this figure on brokerage statements and in a mutual fund’s prospectus. It is essentially the simple average of a series of periodic return growth rates.

One thing to keep in mind is that the periods used should all be of equal length—for instance, years, months, or weeks—and not to mix periods of different duration.

AAGR Example

The AAGR measures the average rate of return or growth over a series of equally spaced time periods. As an example, assume an investment has the following values over the course of four years:

• Beginning value = $100,000
• End of year 1 value = $120,000
• End of year 2 value = $135,000
• End of year 3 value = $160,000
• End of year 4 value = $200,000

The formula to determine the percentage growth for each year is:

$\text{Simple percentage growth or return} = \frac{\text{ending value}}{\text{beginning value}} – 1$Simple percentage growth or return=beginning valueending value​−1

Thus, the growth rates for each of the years are as follows:

• Year 1 growth = $120,000 / $100,000 – 1 = 20%
• Year 2 growth = $135,000 / $120,000 – 1 = 12.5%
• Year 3 growth = $160,000 / $135,000 – 1 = 18.5%
• Year 4 growth = $200,000 / $160,000 – 1 = 25%

The AAGR is calculated as the sum of each year’s growth rate divided by the number of years:

$AAGR = \frac{20 \% + 12.5 \% + 18.5 \% + 25 \%}{4} = 19\%$AAGR=420%+12.5%+18.5%+25%​=19%

In financial and accounting settings, the beginning and ending prices are usually used. Some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed.

As another example, consider the five-year real gross domestic product (GDP) growth for the United States over the last five years. The U.S. real GDP growth rates for 2017 through 2021 were 2.3%, 2.9%, 2.3%, -3.4%, and 5.7%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 1.96%, or (2.3% + 2.9% + 2.3% + -3.4% + 5.7%) / 5.

AAGR vs. Compound Annual Growth Rate

AAGR is a linear measure that does not account for the effects of compounding. The above example shows that the investment grew an average of 19% per year. The average annual growth rate is useful for showing trends; however, it can be misleading to analysts because it does not accurately depict changing financials. In some instances, it can overestimate the growth of an investment.

For example, consider an end-of-year value for year 5 of $100,000 for the AAGR example above. The percentage growth rate for year 5 is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year 1 and the ending value of year 5, the performance yields a 0% return. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR).

The CAGR smooths out an investment’s returns or diminishes the effect of the volatility of periodic returns. 

Formula for CAGR

$CAGR = \frac{\text{Ending Balance}}{\text{Beginning Balance}}^{\frac{1}{\text{\# Years}}} – 1$CAGR=Beginning BalanceEnding Balance​# Years1​−1

Using the above example for years 1 through 4, the CAGR equals:

$CAGR = \frac{\$200,000}{\$100,000}^{\frac{1}{4}}- 1 = 18.92\%$CAGR=$100,000$200,000​41​−1=18.92%

For the first four years, the AAGR and CAGR are close to one another. However, if year 5 were to be factored into the CAGR equation (-50%), the result would end up being 0%, which sharply contrasts the result from the AAGR of 5.2%.

Limitations of the AAGR

Because AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk involved in the investment, as calculated by the volatility of its price. For instance, if a portfolio grows by a net of 15% one year and 25% in the next year, the average annual growth rate would be calculated to be 20%.

To this end, the fluctuations occurring in the investment’s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement.

A second issue is that as a simple average it does not care about the timing of returns. For instance, in our example above, a stark 50% decline in year 5 only has a modest impact on total average annual growth. However, timing is important, and so CAGR may be more useful in understanding how time-chained rates of growth matter.

What Is the Average Annual Return (AAR)?

The average annual return (AAR) is a percentage used when reporting the historical return, such as the three-, five-, and 10-year average returns of a mutual fund. The average annual return is stated net of a fund’s operating expense ratio. Additionally, it does not include sales charges, if applicable, or portfolio transaction brokerage commissions.

In its simplest terms, the average annual return (AAR) measures the money made or lost by a mutual fund over a given period. Investors considering a mutual fund investment will often review the AAR and compare it with other similar mutual funds as part of their mutual fund investment strategy.

Understanding the Average Annual Return (AAR)

When you are selecting a mutual fund, the average annual return is a helpful guide for measuring a fund’s long-term performance. However, investors should also look at a fund’s yearly performance to fully appreciate the consistency of its annual total returns.

For example, a five-year average annual return of 10% looks attractive. However, if the yearly returns (those that produced the average annual return) were +40%, +30%, -10%, +5% and -15% (50 / 5 = 10%), performance over the past three years warrants examination of the fund’s management and investment strategy.

Components of an Average Annual Return (AAR)

There are three components that contribute to the average annual return (AAR) of an equity mutual fund: share price appreciation, capital gains, and dividends.

Share Price Appreciation

Share price appreciation results from unrealized gains or losses in the underlying stocks held in a portfolio. As the share price of a stock fluctuates over a year, it proportionately contributes to or detracts from the AAR of the fund that maintains a holding in the issue.

For example, the American Funds AMCAP Fund’s top holding is Netflix (NFLX), which represents 3.7% of the portfolio’s net assets as of Feb. 29, 2020. Netflix is one of 199 equities in the AMCAP fund. Fund managers can add or subtract assets from the fund or change the proportions of each holding as needed to meet the fund’s performance objectives. The fund’s combined assets have contributed to the portfolio’s 10-year AAR of 11.58% through Feb. 29, 2020.

Capital Gains Distributions

Capital gains distributions paid from a mutual fund result from the generation of income or sale of stocks from which a manager realizes a profit in a growth portfolio. Shareholders can opt to receive the distributions in cash or reinvest them in the fund. Capital gains are the realized portion of AAR. The distribution, which reduces share price by the dollar amount paid out, represents a taxable gain for shareholders.

A fund can have a negative AAR and still make taxable distributions. The Wells Fargo Discovery Fund paid a capital gain of $2.59 on Dec. 11, 2015, despite the fund having an AAR of negative 1.48%.

Dividends

Quarterly dividends paid from company earnings contribute to a mutual fund’s AAR and also reduce the value of a portfolio’s net asset value (NAV). Like capital gains, dividend income received from the portfolio can be reinvested or taken in cash.

Large-cap stock funds with positive earnings typically pay dividends to individual and institutional shareholders. These quarterly distributions comprise the dividend yield component of a mutual fund’s AAR. The T. Rowe Price Dividend Growth Fund has a trailing 12-month yield of 1.36%, a contributing factor to the fund’s three-year AAR of 15.65% through Feb. 29, 2020.

Special Considerations

Calculating an average annual return is much simpler than the average annual rate of return, which uses a geometric average instead of a regular mean. The formula is: [(1+r₁) x (1+r₂) x (1+r₃) x … x (1+r_i)] ^(1/n) – 1, where r is the annual rate of return and n is the number of years in the period.

The average annual return is sometimes considered less useful for giving a picture of the performance of a fund because returns compound rather than combine. Investors must pay attention when looking at mutual funds to compare the same types of returns for each fund.