How to Calculate Annual Percentage Rate (APR)
How APR Describes Loan Costs
Annual Percentage rate (APR) explains the cost of borrowing with a variety of loans, including credit cards and mortgage loans. Costs are quoted as a percentage. For example, if your loan has an APR of 10 percent, you would pay $10 per $100 that you borrow each year. All other things being equal, the loan with the lowest APR is typically least expensive—but it’s usually more complicated than that.
Although APR is not perfect, it provides a starting point for comparing interest and fees from different lenders.
Not just interest: APR is unique because can include fees—in addition to interest charges—and converts the effect of those fees to an annualized cost. This helps you better understand the total cost of borrowing. To use APR properly, it’s essential to understand how it works.
In many cases, your lender provides an APR, but you might need to calculate APR yourself (or you might just want to check their math).
Online calculator: If you just want an APR calculation without doing the math yourself, use this online APR calculator in Google Sheets.
The Value of APR
Loans can be confusing. Slick lenders quote different numbers that mean different things. They might include certain costs that you're likely to pay, or they might omit those costs in advertisements and brochures.
Apples to apples: Even with honest, completely transparent lenders, it can still be hard to tell which loan is least expensive.
Is it better to get a low rate with high fees, or a higher rate with lower fees? APR helps you (more or less) get an apples-to-apples comparison of loans by accounting for all of the costs related to borrowing.
How to Calculate APR
Calculating APR can be tricky, but there are several ways to do it:
- Calculate with spreadsheets like Microsoft Excel or Google Sheets.
- Calculate by hand.
Either way, it’s a two-step process:
- Solve for the monthly payment.
- Calculate the rate using the payment you just calculated and your “amount financed.”
Example: You borrow $100,000 at a 7 percent interest rate using a 30 year fixed rate mortgage. You will pay $1,000 in closing costs. What is the APR?
Answer: The APR in this example is 7.10 percent. Let’s review how to arrive at that rate.
With a spreadsheet (Microsoft Excel and Google Sheets in particular), built-in functions do most of the work for you. Calculating the monthly payment by hand is not difficult, but solving for the rate is best done with a computer or calculator. To start, you need to convert the interest rate from percentage to decimal format.
Step One: Find the monthly payment for your loan:
The spreadsheet function: =PMT(rate,nper,pv,fv,type)
- 0.07 percent divided by 12 is the rate. You’re using a monthly rate to find monthly payments.
- The number of periods is 360. That’s the total number of payments or months (over 30 years in this example).
- The present value of your loan is 100,000, including any additional costs.
You should have a result of $665.30.
Step Two: Solve for the APR:
The spreadsheet formula: =RATE(nper,pmt,pv,fv,type,guess)
- Again, 360 is the number of periods you pay on the loan, given 12 monthly payments over 30 years.
- Your payment is - 665.30. This is a negative number, and it’s from Step One above.
- The present value of your loan is $99,000. This is how much you’re actually borrowing, and explained in greater detail below.
You should have a result of 0.592 percent. This is still a monthly rate. Multiply by 12 to get 7.0999 APR.
Why does the loan amount shrink from $100,000 to $99,000 above? We need to calculate the rate for this step using an adjusted loan balance. To get that number, start with the $100,000 "loan" and subtract the $1,000 in fees required to get that loan.
Calculate APR on Payday Loans
Payday loans are notoriously expensive. These short-term loans might appear to have relatively low rates, but the fees make them problematic. Sometimes even the charges don’t seem terrible: You might gladly pay $15 to get cash quickly in an emergency. However, when you look at these costs in terms of an annual percentage rate, you’ll probably find that there are better ways to borrow.
Example: You get a payday loan for $500, and you pay a fee of $50. The loan must be repaid within 14 days. What is the APR?
The Consumer Federation of America explains how to calculate the APR on a short-term payday loan:
- Divide the finance charge by the loan amount.
- Multiply the result by 365.
- Divide the result by the term of the loan.
- Multiply the result by 100.
To solve the example above:
- $50 divided by $500 equals .01.
- 0.01 multiplied by 365 equals 36.5.
- 36.5 divided by 14 equals 2.6071 (this is your APR in decimal format).
- 2.6071 multiplied by 100 equals 260.71% APR.
With credit cards, APR tells you what interest rate you pay, but it doesn’t include the effects of compounding, so you almost always pay more than the quoted APR. If you only make small (or minimum) payments on your credit card, you pay interest not only on the money you borrowed, but you’ll also pay interest on the interest that was previously charged to you. This compounding effect makes your cost of borrowing higher than you might think. Instead of looking at the APR, APY would be a more accurate description of how much you pay. This might also be referred to as an effective annual rate.
Also, APR for credit cards only includes interest costs—it doesn’t account for the other fees you pay to your credit card company, so you have to research and compare those costs separately. Annual fees, balance transfer fees, and other charges can add up. A card with a slightly higher APR might be better in some cases, depending on how you use your card. In addition, your credit card might have several different APRs, so you pay different rates for different types of transactions.
With mortgage loans, APR is complicated because it does include more than just your interest charges. Any quotes you get might or might not include closing costs that you have to pay or other payments required to get your loan approved (such as private mortgage insurance). Lenders have the ability to choose whether or not certain items are part of the APR calculation, so you have to look carefully if you’re comparing loans.
You can’t simply rely on an APR quote to evaluate a loan. Instead, look at every charge related to your loan to determine if you’re getting a good deal. If you’re comparing lenders, take note of which charges have been included in the quote.
Also, look at the bigger picture. You need to know how long you’ll keep a loan to make the best decision. For example, one-time charges and up-front costs may drive up your immediate costs to borrow—but the APR calculation will assume those charges are spread out over a longer lifetime. As a result, the APR looks lower on long-term loans. If you're going to pay a loan off quickly, APR tends to underestimate the impact of up-front costs. For more discussion, see Get the Wrong Loan by Comparing APR.