A more thorough understanding of how EAR works and how to calculate it can provide you with an accurate way to compare different 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 period. 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 components:
- 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
Examining EAR from the standpoint of a credit card balance can help you see the difference between your APR and EAR. For a balance of $1,000 on a credit card that charges 20% APR, the interest would cost you $200 in one year. However, most credit cards charge compound interest daily, so you 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 advertises a 20% APR has an EAR of 22.13%, and because of that, your yearly interest payment would be $221 instead of $200.
EAR will always be more than APR unless there is only one compounding period annually, in which case they will be the same.
When EAR refers to interest paid to an investor, it operates similarly. If investment A has an annual interest rate of 5% that is compounded monthly and investment B has the same APR but compounds twice a year, investment 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 with an investment of $1,000:
Investment Option A: [1 + (5% / 12)12] – 1 = 5.11%
Investment Option B: [1 + (5% / 2)2] – 1 = 5.06%
In this example, investment A’s starting balance of $1,000 will be worth $1,051 after one year, and investment B will be worth $1,050.60. While that may not seem like a big difference, it can be significant if the original investment is bigger and you invest the money for a decade or more.
Effective Annual Interest Rate vs. APR
EAR accounts for the impact of compounding interest, whereas the more commonly used annual percentage rate (APR)—also known as “nominal interest”—is an annualized rate that does not factor in compounding interest.
APR is a generally accepted rate to use for banks, credit card companies, and other businesses, but it’s important to figure out EAR so you have a more accurate 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:
|APR||EAR Every 6 Months||EAR Quarterly||EAR Monthly||EAR Daily|
You can find EAR calculators online. These provide a quick means of comparing different loans or investment offers.
- Investors or borrowers should determine 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 annually, the EAR will always be higher than the annual percentage rate (APR) because it factors in the impact of compounding.
- More frequent compounding periods means more interest.