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The effective annual interest rate (EAR) is an interest rate that reflects the real-world rate of return on an investment or savings account, as well as the true rate that you owe on a loan or a credit card.
The EAR incorporates the impact of compounding interest over time. It's also sometimes called the effective interest rate, annual equivalent rate or effective annual percentage rate (APR).
What Influences an Effective Annual Interest Rate?
When you shop around for a loan or a credit card, the interest rate is often reflected as the APR. This rate includes interest charges as well as fees. On a credit card, however, the APR you see doesn't necessarily paint a complete picture. If you don't pay your bill in full every month, you may end up paying interest not only on your principal balance but also on the interest that accrued in previous months.
This concept is called compound interest and it can be a good thing if you're earning interest, but not so good if you're paying it.
Since credit card APRs don't account for compounding interest, you'll need to calculate the EAR to find out the account's real-world interest rate based on both the interest rate and compounding period.
The same is true for investments and interest-bearing accounts, which may compound the interest or gains that you earn on top of your principal balance and what you've already earned in the account.
More frequent compounding periods result in a higher EAR. In other words, a savings account that compounds interest daily will generate more interest annually than an account that compounds monthly.
How to Calculate an Effective Annual Interest Rate
Again, the two components of an EAR are the APR and the number of compounding periods. If you don't already have it, you can use an APR calculator to find that rate.
Next, you'll use the following equation, where "i" is the APR and "n" is the number of compounding periods:
EAR = (1 + i/n)n - 1
Let's say you have a $2,000 balance on a credit card with an APR of 15%. A quick calculation using those numbers might cause you to think you'd pay $300 in interest over one year. But credit cards typically compound interest daily, so you'll need to include that in your calculation to determine the true interest rate.
Plugging those numbers into the equation, here's how you'd do the math:
- (1 + (0.15/365))365 - 1
- 1.0004365 - 1
- 1.1618 - 1
Based on those numbers, your EAR is 16.18%, which means the total interest paid over a year would be $323.60.
While the concept works the same whether you're paying interest or earning it, the terms can be a bit different. For example, savings accounts use the term annual percentage yield (APY) instead of APR, and investment accounts may just provide an annual interest rate.
So let's say you're looking at an investment opportunity that offers a 7% annual interest rate that's compounded quarterly. Here's how you'd run the numbers:
- (1 + (0.07/4))4 - 1
- 1.01754 - 1
- 1.07186 - 1
The EAR on the investment is 7.19%, so if you invest $10,000, you'd earn $719 in gains instead of $700.
Why Is the Effective Annual Interest Rate Important?
Whether you're creating a debt payoff plan or a retirement strategy, understanding the EAR is crucial to your approach.
With a loan or credit card, the EAR provides you with the true cost of the debt. For relatively low balances and interest rates, it likely won't be significantly different from the posted APR. But if you have a lot of debt on a credit card, the cost of borrowing could end up being quite a bit more than you think.
On the flip side, if you're planning your approach to retirement, the goal is to find out how much you need to save on a monthly basis to achieve your goal for what you want once you leave the workforce. If you don't include compounding interest, you'll overestimate how much you need to set aside.
Calculating the expected EAR on your investments will give you a much more accurate idea of what you need to save every month to accomplish your goal. Of course, annual returns aren't guaranteed, but working with a good financial advisor can help you come up with good enough assumptions to make the plan work.
Improve Credit to Lower the Effective Annual Interest Rate on Debt
Lenders determine their interest rates based on your creditworthiness, and the lower your credit score, the higher the EAR may be. If you're looking to pay off debt through a consolidation loan or apply for new debt, take some time first to work on your credit to maximize your chances of scoring a low rate.
Start by checking your credit score and credit report, then take steps to address the potential issues you find there. This process can take time but can ultimately save you a lot of money in the long run.