What Is an Effective Annual Interest Rate?
Aneffective annual interest rate is the real return on a savings account or any interest-paying investment when the effects of compounding over time are taken into account. It also reflects the real percentage rate owed in interest on a loan, a credit card, or any other debt.
It is also called the effective interest rate, 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 because it considers the effects of compounding.
- The more frequent the compounding periods, the higher the rate.
- A savings account or a loan may be advertised with both a nominal interest rate and an effective annual interest rate.
- The effective annual interest rate is the rate that should be compared between loans and investment rates of return.
- The effective annual interest rate does not communicate risk, incorporate fees, or factor in tax implications.
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Understanding the Effective Annual Interest Rate
The effective annual interest rate describes the true interest rate associated with an investment or loan. The most important feature of the effective annual interest rate is that it takes into account the fact that more frequent compounding periods will lead to a higher effective interest rate.
Suppose, for instance, you have two loans, each with a stated interest rate of 10%, in which one compounds annually and the other twice yearly. Even though they both have a stated interest rate of 10%, the effective annual interest rate of the loan that compounds twice per year will be higher.
Effective Annual Interest Rate Formula
The following formula is used to calculate the effective annual interest rate:
EffectiveAnnualInterestRate=(1+ni)n−1where:i=Nominalinterestraten=Numberofperiods
What the Effective Annual Interest RateTells You
A certificate of deposit (CD), a savings account, or a loan offer may be advertised with its nominal interest rate and effective annual interest rate. The nominal interest rate does not reflect the effects of compounding interest or even the fees that come with these financial products. The effective annual interest rate is the real return or interest payment.
That’s why the effective annual interest rate is an important financial concept to understand. You can compare various offers accurately only if you know their effective annual interest rates.
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?
In both cases, the advertised interest rate is the nominal interest rate. The effective annual interest rate is calculated by adjusting the nominal interest rate for the number of compounding periods that the financial product will undergo. In this case, that period is one year. The formula and calculations are as follows:
- Effective annual interest rate = ( 1 + ( nominal rate ÷ number of compounding periods ) ) ^ ( number of compounding periods ) - 1
- Investment A = ( 1 + ( 10% ÷ 12 ) ) 12 - 1
- Investment B = ( 1 + ( 10.1% ÷ 2 ) ) 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. This is because Investment B compounds fewer times over the course of the year. Ifan investor were to put $5 million into one of these investments, the wrong decision would cost more than $5,800 per year.
The effective annual interest rate is important because borrowers might underestimate the true cost of a loan without it. And investors need it to project the actual expected return on an investment, such as a corporate bond.
Effect of the Number of Compounding Periods
As the number of compounding periods increases, so does the effective annual interest rate. Quarterly compounding produces higher returns than semiannual compounding, monthly compounding produces higher returns than quarterly, and daily compounding produces higher returns than monthly. Below 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 is a ceiling to the compounding phenomenon. Even if compounding occurs an infinite number of times—not just every second or microsecond, but continuously—the limit of compounding is reached.
With 10%, the continuously compounded effective annual interest rate is 10.517%. The continuous rate is calculated by raising the number “e” (approximately equal to 2.71828) to the power of the interest rate and subtracting one. In this example, it would be 2.71828 ^ (0.1) - 1.
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 the stated interest rate that does not take into account the effects of compounding interest (or inflation). For this reason, it's sometimes also called the "quoted" or "advertised" interest rate.
On the other hand, the EAR considers the effects of compounding interest. It represents the true annual interest rate after accounting for the impact of compounding interest, and it is typically higher than the nominal interest rate.
In this context, the EAR may be used as opposed to the nominal rate when communicating rates in an attempt to lure business. For example, if a bank offers a nominal interest rate of 5% per year on a savings account and compounds interest monthly, the effective annual interest rate will be higher than 5%. Therefore, the bank might consider promoting the account at the EAR because that rate will appear higher.
Understand the psychological marketing approach of communicating effective annual interest rates. For industries that want to boast higher rates, EAR is best. For industries that want to downplay costs, nominal rates are best.
Uses of Effective Annual Interest Rates
Effective annual interest rates are used in various financial calculations and transactions. This includes but isn't necessarily limited to the following types of analysis.
- Investment Analysis: As shown above, EAR compares the returns on different investment opportunities. This can range from stocks, bonds, or savings accounts. By calculating the EAR of each investment, investors can determine which option will provide the highest return over a specific period. However, EAR does not measure risk, liquidity, or other non-return factors.
- Loan and Mortgage Analysis: EAR is used to compare the costs of different loan and mortgage options. Lenders often advertise their loans and mortgages based on their nominal interest rates, but borrowers need to calculate the EAR to accurately determine the total cost of borrowing.
- Credit Card Analysis: EAR is used to calculate the cost of credit card debt. Credit card companies often charge high nominal interest rates, but by calculating the EAR, consumers can see the actual cost of carrying a balance on their credit card (which may intentionally have not been clearly communicated since it will be higher than the nominal rate).
- Inflation Analysis: EAR is used to adjust for inflation when comparing returns on investments or loans over time. Inflation reduces the purchasing power of money, so it's important to calculate the EAR after adjusting for inflation to accurately determine the real return.
Limitations on Effective Annual Interest Rates
Though broadly used across the financial sector, EAR has several downsides. The EAR calculation assumes that the interest rate will be constant throughout the entire period (i.e., the full year) and that there are no fluctuations in rates. However, in reality, interest rates can change frequently and rapidly, often impacting the overall rate of return. Most EAR calculations also do not consider the impact of transaction, service, or account maintenance fees. These can also affect the total return.
EAR calculations usually do not consider the impact of taxes on the returns. Taxes can significantly reduce the actual returns on investments or savings, and it's important to factor them into any analysis. Though a given individual may truly earn at the EAR, their true return may be reduced by 20% or higher based on what individual tax bracket they reside in.
EAR quotes are often unsuitable for short-term investments because there are fewer compounding periods. More often, EAR is used for long-term investments as the impact of compounding may be significant. This approach may limit the vehicles in which EAR is calculated or communicated.
Lastly, as the EAR calculation is a single rate, it does not calculate, communicate, or convey any risk associated with the 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. Just because a vehicle has a higher EAR does not necessarily make it the ideal opportunity for every individual (considering varying investment preferences or risk tolerances).
How Do You Calculate the Effective Annual Interest Rate?
The effective annual interest rate is calculated using the following formula:
EffectiveAnnualInterestRate=(1+ni)n−1where:i=Nominalinterestraten=Numberofperiods
Although it can be done by hand, most investors will use a financial calculator, spreadsheet, or online program. Moreover, investment websites and other financial resources regularly publish the effective annual interest rate of a loan or investment. This figure is also often included in the prospectus and marketing documents prepared by the security issuers.
What Is the Purpose of Effective Annual Interest Rates?
The purpose of the effective annual interest rate is to make interest rates comparable regardless of their compounding periods. Investors, savers, or borrowers can take nominal rates with different compounding periods (e.g., one that compounds weekly, one that compounds monthly) to see which will be most beneficial to them.
What Is a Nominal Interest Rate?
A nominal interest rate does not consider any fees or compounding of interest. It is often the rate stated by financial institutions.
Is It Better to Have a Higher EAR?
It is better for savers/investors to have a higher EAR, though it is worse for borrowers to have a higher EAR. In either situation, the EAR will likely be higher than the nominal rate; it may be more strategic to understand how the EAR has changed in recent history and what future trends look like when evaluating future transactions.
The Bottom Line
Banks and other financial institutions typically advertise their money market rates using the nominal interest rate, which does not consider fees or compounding. The effective annual interest rate does take compounding into account and results in a higher rate than the nominal. The more compounding periods there are, the higher the ultimate effective interest rate.
The higher the effective annual interest rate is, the better it is for savers/investors but worse for borrowers. When comparing interest rates on a deposit or a loan, consumers should pay attention to the effective annual interest rate, not the headline-grabbing nominal interest rate.
