# Understanding Annual Equivalent Rate: Definition, Formula, and Examples

![Annual Equivalent Rate: The interest rate for a savings account or investment product that has more than one compounding period.](https://www.investopedia.com/thmb/MCTepJMbkL_6AcTItDKLLFlQDko=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/aer.asp-final-87ba9d9d18f54b9fa7cb7236aec34e2b.jpg)

*— Investopedia / Jake Shi*

## What Is the Annual Equivalent Rate (AER)?

The Annual Equivalent Rate (AER) provides the actual interest yield of an investment or savings account by considering multiple compounding periods within a year. It gives investors a truer measure of returns, surpassing the nominal interest rate, by calculating compounded interest. This article will explain the formula for AER and illustrate its application with examples, helping you make informed decisions on investment products.

### Key Takeaways

*   The Annual Equivalent Rate (AER) represents the actual interest rate when considering compounding within a year.
*   AER is higher than the nominal interest rate if there are multiple compounding periods annually.
*   Investors use AER to compare banking products and investments for better returns.  
    Calculating AER involves considering how many times interest is compounded in a year.
*   AER helps investors evaluate the true return on investments despite not accounting for fees.

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](https://www.investopedia.com/terms/e/effectiveinterest.asp) or the [annual percentage yield](https://www.investopedia.com/terms/a/apy.asp) (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. Investors can use AER to compare banking products to find the best [savings accounts](https://www.investopedia.com/high-yield-savings-accounts-4770633) or investment vehicles.

## Understanding the AER Formula

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

## Calculating the AER: A Step-by-Step Guide

How to calculate AER:

1.  Divide the stated interest rate by the number of compounding periods per year and add one.
2.  Raise the resulting value to the power of the number of compounding periods per year.
3.  Subtract one from the final result to get the AER.

The AER is displayed as a percentage (%).

## AER in Action: Example

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.

> **Important**
>
> The stated interest rate paid on an account offering monthly interest may be lower than the rate on an account offering only one interest payment per year. However, when interest is compounded, the former account may offer higher returns than the latter account. For example, an account offering a rate of 6.25% paid annually may look more attractive than an account paying 6.12% with monthly interest payments. However, the AER on the monthly account is 6.30%, as opposed to an AER of 6.25% on the account with annual interest payments.

Bank A's annual equivalent rate is 3.7%, calculated as (1 + (0.037 / 1))^1 - 1. Bank B has an AER of 3.65% = (1 + (0.0365 / 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.

Bank C also has a 3.7% interest rate like Bank A, but 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)) - 1 = 3.73%.

### With a Bond

Let's now consider a bond issued by General Electric. In March 2019, General Electric offered a [noncallable](https://www.investopedia.com/terms/n/noncallable.asp) 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+ (0.08 / 2 )) - 1 = 8.16%.

## Comparing AER and Stated Interest Rates

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.

## Pros and Cons of Using AER

The main advantage of AER is that it reflects the true interest rate by accounting for compounding. It also helps investors evaluate bonds, loans, or accounts to understand their actual return on investment (ROI).

Unfortunately, AER is often not provided when evaluating different investments. 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.

Pros of AER

*   Unlike the APR, AER reveals the actual interest rate.
    
*   Crucial in finding the true ROI from interest-bearing assets. 
    

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.
    

## Important Factors When Considering AER

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](https://www.investopedia.com/terms/p/principal.asp) 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.

Warren Buffett once said, "My wealth has come from living in America, some lucky genes, and [compound](https://www.investopedia.com/terms/c/compounding.asp) interest." Albert Einstein reportedly referred to [compound interest](https://www.investopedia.com/terms/c/compoundinterest.asp) as mankind's greatest invention. 

When borrowing money through loans, try to minimize compounding effects. 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.

## Where Can I Find an AER Calculator Online?

There are many websites that offer tools for calculating AER, including the websites [Calculator Soup](https://www.calculatorsoup.com/calculators/financial/effective-annual-rate-calculator.php), [Get Calc](https://getcalc.com/finance-annual-effective-rate-calculator.htm), and [Omni Calculator](https://www.omnicalculator.com/finance/equivalent-rate).

## What Is a Nominal Interest Rate?

The nominal interest rate is the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest. The nominal interest rate is what is specified in the loan contract, without adjusting for compounding. Once 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 remove the effects of inflation. Real interest rates reflect the real [cost of funds](https://www.investopedia.com/terms/c/costoffunds.asp), in the case 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](https://www.investopedia.com/terms/n/nominalinterestrate.asp) and the inflation rate.

## The Bottom Line

The Annual Equivalent Rate (AER) is crucial for understanding the true yield or cost of financial products, as it accounts for compounding interest. When an interest rate compounds multiple times a year, the AER provides a more accurate figure than the nominal rate, allowing investors to compare financial products effectively. By understanding AER, both investors and borrowers can make informed decisions on savings accounts, bonds, and loans, maximizing returns or minimizing costs.

> **Article Sources**
>
> 1.  The Giving Pledge. "[My philanthropic pledge](https://givingpledge.org/pledger?pledgerId=177#:~:text=The%20asset%20I%20most%20value,I%20call%20the%20ovarian%20lottery.)."
>     
> 2.  Inc. “[Why Einstein Considered Compound Interest the Most Powerful Force in the Universe](https://www.inc.com/jim-schleckser/why-einstein-considered-compound-interest-most-powerful-force-in-universe.html).”