What Is Effective Annual Interest Rate?

Effective Interest Rate Explained

Effective annual rate (EAR) is an interest rate that reflects the true return on an investment or the true amount of interest due on a credit card or loan.

A more thorough knowledge of how EAR works and how to calculate it can provide you with an accurate way to compare credit cards, loans, and investments that have annual interest rates and different compounding periods.

What Is Effective Annual Interest Rate?

EAR is the interest rate that factors in compounding interest (interest charged on interest) over a given amount of time. For example, a balance due on a credit card may include interest. If you don’t pay off the balance by the due date, the issuer will charge interest on the existing interest.

• Alternative names: Effective interest rate, annual equivalent rate, effective APR
• Acronyms: EAR, EIR, AER

How To Calculate Effective Annual Interest Rate

The equation for calculating EAR has two main parts: 

• i: the stated interest rate (APR)
• n: the number of compounding periods

Here’s how the equation looks before you plug in your APR and compounding periods:

EAR = (1 + i/n)n – 1

Credit Card EAR

When you look at EAR from the standpoint of a credit card balance, you can see how your APR and EAR differ. For a balance of $1,000 on a credit card that charges 20% APR, the interest would cost you $200 in one year. But take note that most credit cards charge compound interest daily, This means you have to calculate the EAR for the same $1,000 balance like this:

[1 + (20% / 365)365] – 1 = .2213 or, expressed as EAR, 22.13%

In this example, a credit card that claims to have a 20% APR really has an EAR of 22.13%. For this reason, your yearly interest payment would be $221 instead of $200.

Note

EAR will always be more than APR unless there is only one compounding period annually. If there is only one, in this case they will be the same.

Investment EAR

When EAR refers to interest paid to an investor, it works much the same way. Suppose you invest in stock fund A, which has an annual interest rate of 5% that is compounded monthly. Stock fund B has the same APR but compounds twice a year. Of these two, option A will have a higher overall return or yield because it compounds more often.

Here’s how to calculate the difference between the two options if you start by investing $1,000 into both A and B:

Option A: [1 + (5% / 12)12] – 1 = 5.11%

Option B: [1 + (5% / 2)2] – 1 = 5.06%

In this example, stock fund A’s starting balance of $1,000 will be worth $1,051 after one year. Stock fund B will be worth $1,050.60. While that may not seem like a big difference, it can add up to quite a bit, especially if you invest more money at first and you keep the fund for a decade or more.

Effective Annual Interest Rate vs. APR

As explained above, EAR accounts for the impact of compounding interest. But it is more common to hear about annual percentage rate (APR) (also known as “nominal interest”). This is an annualized rate that does not factor in compounding interest.

For the most part, banks, credit card companies, and other businesses use APR when touting their products. But if you are looking into a credit card or any other product, it’s crucial to figure out EAR as well. This will give you a much better idea of how interest will affect the outcome of carrying a balance or holding an investment like a CD or money market account.

The table below compares EAR to four different APRs over four different compounding periods:

You can find EAR calculators online. These provide a quick means of comparing more than loans or investment offer side by side.

Key Takeaways

• When investing or borrowing you should figure out the effective annual interest rate (EAR) because it provides the true return on a fixed-rate investment or the actual amount of interest due on a loan.
• Unless interest is only compounded once per year, the EAR will always be higher than the annual percentage rate (APR) because it factors in the impact of compounding.
• The more often interest is compounded, the greater the interest charges will be.

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1. Corporate Finance Institute. "Effective Annual Interest Rate."