# Effective Annual Interest Rate: Definition, Formula, and Example

> **Definition**
>
> The effective annual interest rate is the compounded interest rate paid on an investment or the real rate of interest paid on a debt.

## What Is the Effective Annual Interest Rate?

The effective annual interest rate is the actual return on a savings account or other interest-bearing investment when the effects of compounding are considered. It also is the real percentage rate paid in interest on a loan or other debt.

The effective annual interest rate is sometimes called the effective rate or the annual equivalent rate (AER).

### Key Takeaways

*   The effective annual interest rate is the true interest rate on an investment or loan.
*   A savings account or a loan may be advertised with both a nominal interest rate and an effective annual interest rate.
*   Consumers can compare effective annual interest rates offered by competing banks.
*   Effective annual interest rates don't factor in fees or tax implications.

![Effective Annual Interest Rate](https://www.investopedia.com/thmb/9v29cZ8M3l1CmoJKWSw0cJ1kzl4=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/effectiveinterest-Final-91fa363e000e4f4e847a240a3e8cd358.jpg)

*— Theresa Chiechi / Investopedia*

## How the Effective Annual Interest Rate Works 

The effective annual interest rate describes the actual interest rate that's associated with a financial product or loan. The most important aspect of effective annual interest rates is that they account for the fact that more frequent compounding periods will lead to a higher effective [interest rate](https://www.investopedia.com/terms/i/interestrate.asp).

Suppose you have two loans, each with an interest rate of 10%. One compounds annually and the other compounds twice yearly. They both have a stated interest rate of 10% but the effective annual interest rate on the loan that compounds twice a year will be higher.

This bar chart shows how different compound periods make a difference over 10 years with 10% on an initial $1,000.00.

## Effective Annual Interest Rate Formula 

The following formula is used to calculate the effective annual interest rate:

$\begin{aligned} &Effective\ Annual\ Interest\ Rate=\left ( 1+\frac{i}{n} \right )^n-1\\ &\textbf{where:}\\ &i=\text{Nominal interest rate}\\ &n=\text{Number of periods}\\ \end{aligned}$  

## Example of Effective Annual Interest Rate

Consider these two offers: Investment A pays 10% interest, compounded monthly. Investment B pays 10.1%, compounded semiannually. Which is the better offer?

The advertised interest rate is the nominal interest rate in both cases. The effective annual interest rate is calculated by adjusting the nominal interest rate for the number of compounding periods for the compounding product. That period is one year in this case. These are the formula and calculations:

*   Effective annual interest rate = (1 + (nominal rate ÷ number of compounding periods)) – 1
*   Investment A = (1 + (10% ÷ 12 )) – 1
*   Investment B = (1 + (10.1% ÷ 2)) – 1
*   Investment A = 10.47%
*   Investment B = 10.36%

Investment B has a higher stated nominal interest rate but the effective annual interest rate is lower than the effective rate for investment A because Investment B compounds fewer times over the year.

Let's assume that you invest $5 million. The annual compounding result for Investment A is $523,500 in this example: $5 million × 10.47%.

The result for Investment B is $518,000: $5 million × 10.36%.

The wrong decision (choosing Investment B instead of Investment A) would effectively cost $5,500 ($523,500 minus $518,000) if an investor were to put $5 million into one of these investments.

> **Important**
>
> The effective annual interest rate is important because borrowers might underestimate the true cost of a loan without it. Investors need it to project the actual expected return on an investment, such as a corporate bond.

## Consideration for Loan Payments

EAR is also crucial for borrowers because it reveals the actual cost of a loan by accounting for compounding periods. A higher EAR means more frequent compounding, leading to higher overall interest costs than the nominal rate suggests. This affects the total amount repayable.  

Focusing on the EAR rather than the nominal rate is essential for borrowers comparing loan offers. It ensures a more accurate comparison of loan costs, highlighting the impact of different compounding frequencies on the total interest paid over time. This ultimately aids in making more informed financial decisions.

## Effect of Compounding Periods

The effective annual interest rate increases as the number of [compounding periods](https://www.investopedia.com/terms/c/compoundinterest.asp) increases. Quarterly compounding produces higher returns than semiannual compounding. Monthly compounding produces higher returns than quarterly and daily compounding produces higher returns than monthly.

This is a breakdown of the results of these different compound periods with a 10% nominal interest rate:

*   Semiannual = 10.250%
*   Quarterly = 10.381%
*   Monthly = 10.471%
*   Daily = 10.516%

### Limits to Compounding

There's a ceiling to the effects of compounding. The limit of compounding is reached if compounding occurs an infinite number of times, not just every second or microsecond, but continuously.

The [continuously compounded](https://www.investopedia.com/terms/c/continuouscompounding.asp) effective annual interest rate is 10.517% with 10%. The continuous rate is calculated by raising the number “e” (about 2.71828) to the power of the interest rate and subtracting one. It would be 2.71828 – 1 in this example.

> **Tip**
>
> EAR is best for industries that want to boast higher rates. Nominal rates are best for industries that want to downplay costs. Pay attention to which is being used when you look at marketing materials.

## Effective Annual Interest Rate vs. Nominal Interest Rate

The primary difference between an effective annual interest rate and a nominal interest rate is the compounding periods. The nominal interest rate is a stated interest rate that doesn't take the effects of compounding interest or [inflation](https://www.investopedia.com/terms/i/inflation.asp) into account. It's sometimes also referred to as the "quoted" or "advertised" interest rate for this reason.

The EAR accounts for the effects of compounding interest. It's the true annual interest rate after accounting for the impact of compounding interest which is typically higher than the nominal interest rate.

The EAR may be used rather than the nominal rate when communicating rates in an attempt to lure business. The effective annual interest rate will be higher than 5% if a bank offers a nominal interest rate of 5% per year on a savings account and compounds interest monthly. The bank might therefore consider promoting the account at the EAR because that rate will appear higher.

### Key Differences – Effective Annual Interest Rate vs. Nominal Interest Rate

Effective Annual Interest Rate

*   Accounts for compounding periods  
    
*   Is the true annual rate
    
*   Typically higher than the nominal rate
    

Nominal Interest Rate

*   Stated interest rate
    
*   Ignores compounding effects
    
*   Also called "quoted" rate
    

## Uses of Effective Annual Interest Rates

Effective annual interest rates are used in several financial calculations and transactions.

*   **Investment analyses**: EAR compares the returns on different investment prospects including stocks, bonds, or savings accounts. Investors can determine which option will give the highest return over a specific period by calculating the EAR of each financial product. EAR doesn't measure risk, [liquidity](https://www.investopedia.com/terms/l/liquidity.asp), or other non-return factors, however.
*   **Loan and mortgage analysis**: EAR compares the costs of loan and mortgage options. Lenders often advertise their loans and mortgages based on their nominal interest rates but borrowers have to calculate the EAR to accurately determine the total cost of borrowing.
*   **Credit cards**: EAR calculates the cost of credit card debt. Credit card lenders often charge high nominal interest rates. Consumers can see the actual cost of carrying a [balance on their credit card](https://www.investopedia.com/terms/c/credit-card-balance.asp) which may intentionally not be clearly communicated by calculating the EAR.
*   **Inflation analysis**: EAR adjusts for inflation when comparing returns on investments or loans over time. Inflation reduces the purchasing power of money so it's essential to calculate the EAR after adjusting for inflation to accurately determine the actual return.

## Limitations of Effective Annual Interest Rates

EAR is broadly used across the financial sector, but it has several downsides. The EAR calculation assumes that the interest rate will be constant throughout the entire period and that there are no fluctuations in rates. Interest rates can change frequently and rapidly, however, and this often impacts the overall rate of return. Most EAR calculations don't consider the impact of transaction, service, or account maintenance fees, either. These can also affect the total return.

EAR calculations usually don't consider the impact of taxes on returns. Taxes can significantly reduce the actual returns on investments or savings, and it's important to factor them into any analysis. An individual may truly earn at the EAR, but their true return can be reduced by 20% or more based on their [tax bracket](https://www.investopedia.com/terms/t/taxbracket.asp).

EAR quotes are often unsuitable for short-term investments because there are fewer compounding periods. EAR is used for long-term investments more often because the impact of compounding can be significant. This approach may limit the vehicles in which EAR is calculated or communicated.

The EAR calculation is a single rate, so it doesn't calculate, communicate, or convey the risks of an investment or loan. Higher returns often come with higher risk, and it's important to consider the risk associated with an investment or loan before deciding.  

## How Will I Use This in Real Life?

You might see [certificates of deposit](https://www.investopedia.com/terms/c/certificateofdeposit.asp), savings accounts, or loan offers advertised with both their nominal interest rates and their effective annual interest rates. The nominal interest rate doesn't reflect the effects of compounding interest or the fees for these financial products, so it's unlikely to give you a fully accurate picture of how much you can potentially earn. Effective annual interest rates are real returns or interest payments.

Effective annual interest rates are essential. They allow you to compare various offers accurately.

## What Is the Discount Yield?

The discount yield is the annualized return on a discount bond, such as a [Treasury bill](https://www.investopedia.com/terms/t/treasurybill.asp). It's calculated as the difference between the face value and the purchase price divided by the face value and adjusted for the number of days to maturity.

## What Is the Yield to Maturity?

This is the total return expected on a [bond](https://www.investopedia.com/terms/b/bond.asp) if it's held until maturity. It accounts for all coupon payments received over the bond's life and any capital gain or loss.  

## Is It Better to Have a Higher EAR?

Savers or investors should have a higher EAR but it's worse for borrowers. The EAR will likely be higher than the nominal rate in either case, however. It may be more strategic to understand how the EAR has changed and what trends look like when you're evaluating future transactions.

## The Bottom Line

Banks and other financial institutions typically advertise their [money market](https://www.investopedia.com/terms/m/moneymarket.asp) rates using the nominal interest rate which doesn't consider fees or compounding. The effective annual interest rate does take compounding into account and it results in a higher rate than the nominal. The more compounding periods there are, the higher the ultimate effective interest rate will be.

Consumers should pay attention to the effective annual interest rate, not the headline-grabbing nominal interest rate when they're comparing interest rates on a deposit or loan.  

> **Article Sources**
>
> 1.  Rober Parrino et al. "[Fundamentals of Corporate Finance](https://www.google.com/books/edition/Fundamentals_of_Corporate_Finance/QPk_EAAAQBAJ?hl=en&gbpv=1&dq=Corporate+Finance&printsec=frontcover)." Sections 14-20_,_ John Wiley & Sons, 2022.
>     
> 2.  Sunil Parameswaran. "[Fundamentals of Financial Instruments: An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives](https://onlinelibrary.wiley.com/doi/book/10.1002/9781119816621)." Pages 55–57 and 62. John Wiley & Sons, 2022.
>     
> 3.  Sunil Parameswaran. "[Fundamentals of Financial Instruments: An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives](https://onlinelibrary.wiley.com/doi/book/10.1002/9781119816621)." Pages 146–153. John Wiley & Sons, 2022,