# EAR vs. APR: What are the differences between EAR and APR?

If you're in the market for a business loan, you've probably seen a dizzying array of acronyms like APR, APY, and EAR. Understanding the subtle difference between them can mean the difference between securing funding at a competitive rate or getting stuck with a costly loan. This guide will introduce you to APR and EAR, as well as what matters most when you need financing to grow your business.

## What is APR?

Annual percentage rate (APR) is a figure that appears alongside a wide range of lending products, from home mortgages to credit cards. It refers to the annual percentage rate, which represents the total annual interest you pay on a loan (or earn through an investment).

In lending, APR simply expresses the cost of borrowed funds over the course of a year. For example, if you borrowed \$10,000 at 10% APR for one year, the annual cost of that \$10,000 principal loan would be \$1,000 in interest payments, a total repayment of \$11,000. APR can also be used to calculate the monthly payment. To repay the loan in 12 monthly installments would equal a payment of \$916 per month.

APR usually includes any fees or closing costs incurred as part of securing the loan as well. However, APR does not include compound interest, which is the interest charged on top of the principle plus accumulated interest.

## How to calculate APR

APR is expressed by the following formula, which calculates the periodic interest rate and then multiplies it by the number of periods per year that interest is applied to the loan. In this case, interest is applied every day. The resulting number is then expressed as a percentage.

The mathematic formula for calculating APR is:

APR = [(i / p) / n] x 365 x 100

i = total interest paid over the life of the loan (plus fees)

p = principal amount of loan

n = number of days in the term

Here, the periodic interest rate is the part of the formula that reads [(i / p) / n]. Once this number is determined, it is multiplied by the number of times per year that rate is applied to the principal balance of the loan, which is 365 days. The resulting number is a decimal point that can be expressed as a percentage by multiplying by 100.
So, in the hypothetical loan example above, the formula would look like:

10% = [(\$1,000/\$10,000) / 365] x 365 x 100

Ultimately, while APR serves as a simple barometer of how much you can expect to pay each year on a loan, it is not sufficient to tell the whole story. To really understand how much money you’re spending on interest over time, you must calculate the EAR.

## What is EAR?

EAR stands for "effective annual rate," and is also referred to as annual percentage yield (APY). Unlike APR, EAR includes compound interest over time, which can add up to rather significant sums. Compound interest is the interest charged on top of both the principle and previously accumulated interest, further increasing the amount a borrower owes or a saver receives.

For example, a one-year loan of \$10,000 with an APR of 12% that compounds once per month would accrue interest as follows:

• In the first month of the loan, the borrower would be charged 1% interest on the principal amount of \$10,000, increasing the outstanding balance to \$10,100.
• In subsequent months, the 1% monthly interest rate would apply to the outstanding balance of \$10,100 instead of the principal balance of \$10,000, resulting in a \$101 interest charge and increasing the balance to \$10,201.
• Interest continues to compound throughout the life of the loan, building on top of the accrued balance. In this example, the effective annual rate would be about 12.7%, rather than the advertised APR of 12%.

Understanding the effective annual rate of a loan can help you make a more informed decision about the true long-term costs of funding. It also means that an APR and EAR can represent the same thing; in this case, a 12% APR is equal to a 12.7% EAR. As a result, banks tend to advertise APR when offering loans and EAR (or APY) when offering savings accounts.

## How to calculate EAR

To calculate EAR, use the following formula:

APY = 100 [(1 + r / n)^n] -1

r = annual interest rate (or the APR)

n = number of compounding periods per year

So, for the loan in the example above, where the APR is 12% (or 0.12), and interest is compounded 12 times per year, the formula would be expressed as:

12.7% = 100 [(1 + 0.12 / 12)^12] -1

APY is a more accurate measure of the true cost of borrowing over time. If you are trying to project the cost of your business loan over the entirety of the term, you want to find an effective annual rate.

## What's the difference between EAR and APR?

APR is the simple interest rate charged on borrowed funds over the course of the year. It is more frequently the percentage used to compare loans and credit cards quickly because it also accounts for fees and closing costs. It is most effective for loans like fixed-rate mortgages, which have a balance that doesn't fluctuate like revolving credit. However, the APR does not account for compound interest.

EAR calculates compound interest and serves as a more accurate representation of the cost of borrowing money over time. On a credit card, for example, carrying a balance month over month will increase the EAR, resulting in a higher rate than the advertised APR. Additionally, EAR is determined by the number of compounding periods per year. When accepting a loan, for example, 12 compounding periods will always result in a higher EAR than a loan that compounds quarterly.