How to Calculate Annual Percentage Rate (APR)

The APR helps evaluate loan costs

Image by Emily Roberts © The Balance 2019

The annual percentage rate (APR) of a loan is the interest you pay each year represented as a percentage of the loan balance. For example, if your loan has an APR of 10%, you would pay $100 annually per $1,000 borrowed. All other things being equal, the loan with the lowest APR is typically the least expensive, but it’s usually more complicated than that.

Although APR is not perfect, it provides a helpful starting point for comparing interest and fees from different lenders.

For quick APR calculations, create a spreadsheet with the appropriate formulas or download an existing spreadsheet and adjust it for your needs.

Understanding APRs

APRs include fees in addition to interest charges and convert those fees to an annualized cost. Understanding how APRs work helps you to better understand the total cost of borrowing.

Don't assume the lender with the lowest interest rate is the least expensive option. Calculate your APR, which includes all associated fees, to help you identify the best deal.

Lenders often quote different numbers that mean different things. Some might quote interest rates without including additional fees in their advertisements, while others might list everything upfront. Even with honest, completely transparent lenders, it still can be difficult to tell which loan is the least expensive. APRs help you get an apples-to-apples comparison of loans by accounting for every cost related to borrowing.

Calculate Monthly Payment

The first step to calculating your APR is figuring out the amount of your monthly payment (p) using your principal balance or total loan amount (a), periodic interest rate (r), which is your annual rate divided by the number of payment periods, and your total number of payment periods (n):

  • Formula: a/{[(1+r)^n]-1}/[r(1+r)^n]=p

Let's say you borrow $100,000 with a 7% interest rate using a 30-year fixed-rate mortgage. To calculate the monthly payment, convert percentages to decimal format, then follow the formula:

  • a: 100,000, the amount of the loan
  • r: 0.00583 (7% annual rate—expressed as 0.07—divided by 12 monthly payments per year)
  • n: 360 (12 monthly payments per year times 30 years)
  • Calculation: 100,000/{[(1+0.00583)^360]-1}/[0.00583(1+0.00583)^360]=665.30, or 100,000/150.3081=665.30

The monthly payment is $665.30. Check your math with an online payment calculator.

Microsoft Excel and Google Sheets, among others, provide built-in functions that do most of the work for you. In Excel, for example, you can calculate your monthly payment by typing the following formula into a cell:

  • =PMT(rate/number of annual payments, the total number of payments, loan amount)

For the example above, the formula would look like this:

  • =PMT(0.07/12,360,100000)

Calculate Your APR

Following the same example, use the monthly payment you calculated plus any upfront fees rolled into the $100,000 you borrowed to calculate your APR. If $1,000 of the amount borrowed was used for closing costs, the value of the loan is $99,000, and that is the amount used to calculate the APR.

Again, spreadsheets like Excel make this calculation easy. Simply type the following formula into a cell:

  • =RATE(total number of payments, -monthly payment, loan value)

For this example, the formula would look like this:

  • =RATE(360,-665.30,99000)

Note that the monthly payment is represented as a negative number based on the previous calculation used to determine the amount.

You should get a result of 0.5917%. This is still a monthly rate, so multiply it by 12 to get 7.0999%, which is your APR.

Calculate Your APR on Payday Loans

Payday loans might appear to have relatively low rates, but the fees typically make the overall cost of borrowing quite high. Sometimes the charges don’t seem terrible. You might gladly pay $15 to get cash quickly in an emergency, for example. However, when you look at these costs in terms of an APR, you may find that there are less expensive ways to borrow.

For example, a $500 payday loan that must be repaid within 14 days with a $50 fee has an APR of 260.71%. The Consumer Federation of America explains how to calculate it:

  1. Divide the finance charge by the loan amount. In this case, $50 divided by $500 equals 0.1.
  2. Multiply the result by 365 to get 36.5.
  3. Divide the result by the term of the loan. In this case, 36.5 divided by 14 is 2.6071.
  4. Multiply the result by 100 to turn the answer into a percentage: 260.71%.

APRs on Credit Cards

With credit cards, your APR tells you the interest payments, but it doesn’t include the effects of compounding interest, so you almost always pay more than the quoted APR.

If you carry a balance on your credit card, you pay interest on the money you borrowed and on the interest that already has accrued. This compounding effect makes your cost of borrowing higher than you might think.

The APR for credit cards includes interest costs but not the other fees you pay to your credit card issuer, so you have to research and compare those fees separately. Annual fees, balance transfer fees, and other charges can add up. As a result, a card with a slightly higher APR might be better, depending on how you use your card. In addition, your credit card might have different APRs for different types of transactions.

APRs and Home Loans

With mortgages, APR is complicated because it includes more than just your interest charges. Any quotes you get may or may not include closing costs you have to pay. Plus, you may have to make additional payments to qualify for the loan, such as private mortgage insurance. Lenders can choose whether or not certain items are part of the APR calculation, so you have to look carefully and know how to do your own calculations.

It's also important to know how long you’ll keep a loan to make the best decision. For example, one-time charges and upfront costs may drive up your immediate costs to borrow, but the APR calculation assumes you spread those charges out over the full term of your loan. As a result, the APR appears lower on long-term loans. If you plan to quickly pay off a loan, APR typically underestimates the impact of upfront costs.

Article Sources

  1. Consumer Financial Protection Bureau. "What Is the Difference Between a Mortgage Interest Rate and an APR?" Accessed March 10, 2020.

  2. California State Board of Equalization. "Lesson 7: Periodic Repayment (Assessors’ Handbook 505, Column 6)." Accessed March 10, 2020.

  3. Microsoft. "PMT Function." Accessed March 10, 2020.

  4. "Payday Loans and Cash Advances." Accessed March 10, 2020.

  5. Consumer Federation of America. "How to Calculate the Interest on Payday Loan." Accessed March 10, 2020.

  6. American Express. "APY vs. APR: The Basics About How Interest Is Calculated." Accessed March 10, 2020.

  7. Federal Reserve Bank of St. Louis. "A Closer Look at Credit Card Disclosures." Accessed March 10, 2020.

  8. Consumer Financial Protection Bureau. "What Costs Will I Have to Pay as Part of Taking Out a Mortgage Loan?" Accessed March 10, 2020.

  9. Consumer Financial Protection Bureau. "How Do I Find the Best Loan Available When I'm Shopping for a Home Mortgage Loan?" Accessed March 10, 2020.