What Is the Annual Percentage Rate (APR)?
The annual percentage rate (APR) is the yearly cost of a loan, including both the interest and the fees the lender charges to give you the loan. Because it rolls the fees into one rate, the APR shows the real cost of borrowing and lets you compare loans that have different rates and fees. In the U.S., the Truth in Lending Act requires lenders to show the APR for mortgages, car loans, personal loans and credit cards.
APR vs interest rate
- Interest rate: the yearly percentage charged on the amount you owe. It does not include fees.
- APR: the interest rate plus the finance fees, expressed as one yearly rate. If a loan has finance fees, its APR is higher than its interest rate; with no fees the two are the same.
Which fees count
- Finance charges raise the APR: origination fees, discount points, mortgage broker fees and other charges you pay to get the loan. They can be added to the loan or paid up front in cash (prepaid).
- Non-finance charges do not raise the APR: costs you would pay even in a cash purchase, such as title, appraisal and recording fees. If they are added to the loan, they raise your payment but not the APR.
APR is not the same as APY (annual percentage yield). APY includes the effect of compounding and is mostly used for savings; APR is the yearly rate quoted on loans.
How to Calculate APR
There is no single formula for APR; it is found in three steps.
Step 1: the payment
The payment is worked out on the loan amount plus any fees added to it, at the interest rate per payment period. If interest compounds at a different frequency than you pay, the rate is converted first:
Where r is the yearly interest rate as a decimal, m the number of times interest compounds a year, p the number of payments a year and n the number of payments.
Step 2: the amount financed
This is the money you actually get to use: the loan plus non-finance fees you borrowed, minus finance fees you prepaid.
Step 3: the rate that matches
Find the rate per period x at which your payments are worth exactly the amount financed. The APR is that rate times the number of payments a year:
This can't be solved directly, so the calculator narrows in on x step by step until the two sides match to a fraction of a cent.
Example
A $10,000 loan at 5% interest, 24 monthly payments, with a $200 origination fee added to the loan:
- i = 5% ÷ 12 = 0.0041667 per month (interest compounds monthly, the same as the payments)
- PMT on $10,200 over 24 months = $447.49
- Amount financed = $10,000 (the $200 fee is a finance charge, not money you get to use)
- Rate per month where 24 payments of $447.49 are worth $10,000: x = 0.5790%
- APR = x × 12 = 6.95%, against the 5% interest rate
The fee adds 1.95 percentage points a year here because it is spread over only two years. The same $200 on the calculator's 5-year default loan adds only 0.55 percentage points.
How to Use the APR Calculator
"I've been offered a $15,000 loan at 5% for 5 years with a $200 origination fee. What does it really cost me per year?" This calculator answers that.
Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own loan offer.
- Loan Amount: Enter 15,000, which is the amount you borrow, before any fees. It must be greater than 0 and less than 1 billion.
- Interest Rate: Enter 5, which is the yearly interest rate the lender quotes, in percent. It can be from 0 to 99.99.
- Interest Compounding: Leave it at Monthly, which is how often interest is added. Most loans with monthly payments compound monthly; you can also pick Daily, Quarterly or Yearly.
- Financial Fees: Enter 200, which is the finance fees added to the loan, such as an origination or broker fee. They raise your APR. Enter 0 if there are none.
- Payment Frequency: Leave it at Monthly, which is how often you make a payment. You can also pick Daily, Quarterly or Yearly.
- Non-Financial Fees: Enter 0, which is fees added to the loan that are not finance charges, such as title or appraisal fees. They raise your payment but not your APR. Enter 0 if there are none.
- Number of Payments: Enter 60, which is how many payments you make in total: 5 years × 12 months. For a 30-year mortgage with monthly payments, enter 360. It must be a whole number from 1 to 1,200.
- Prepaid Financial Fees: Enter 0, which is finance fees you pay in cash when the loan starts, such as discount points. They also raise your APR. Enter 0 if there are none.
Each fee must be 0 or more and less than the loan amount. Not sure what a box means? Hover over or tap the i next to its name for a short explanation.
Calculate and Reset
Click Calculate to see your results. If a box has a problem, such as a letter in a number box, a message pops up under that box instead. With the default numbers you get:
- Your Results: a short summary in words: an APR of 5.55% against the 5% interest rate, the $286.84 monthly payment, and the $2,210.57 cost of borrowing split into interest and fees.
- APR: the headline number, 5.55%.
- Payment per month, Total Payments, Finance Charges and Amount Financed: $286.84 a month, $17,210.57 in total, $2,210.57 of finance charges, on $15,000.00 financed.
- Where the money goes: a ring chart splitting everything you pay into the loan amount, interest and fees. Hover over a part to see its amount and share.
- Interest rate vs APR: two bars that show how much the fees add to the rate.
- Loan breakdown: the APR, payment, total payments, loan with fees added, amount financed, interest, finance fees and finance charges in one table.
- Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.
Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put every box back to its default and show the default results again.