What is APR?
The annual percentage rate (APR) is the yearly cost of a loan including its fees, not just the interest. Two loans with the same interest rate can have different APRs when one of them charges more in fees, so the APR is the fair way to compare offers. In the United States, lenders must show the APR under the Truth in Lending Act.
This APR calculator finds the real APR: the rate at which your payments repay only the money you actually receive, after the fees are taken out. Use General APR for any loan, with any compounding and payment frequency, and Mortgage APR for a home loan with points and mortgage insurance.
Key terms
- Loaned fees are added to the loan balance, so you pay interest on them.
- Upfront fees are paid out of pocket when the loan is made and reduce the money you effectively receive.
- Points are prepaid interest. One point costs 1% of the mortgage amount and usually buys a lower rate.
- PMI is mortgage insurance charged when the down payment is under 20%. It stops once you owe 80% of the house value or less.
How APR is calculated
First the payment is found from the loan amount, the interest rate and the term, with the standard loan payment formula. Then the calculator looks for the monthly rate r at which those same payments are worth only the money you receive:
Loan amount − fees = M / (1 + r) + M / (1 + r)2 + … + M / (1 + r)n
Here M is the monthly payment and n the number of payments. There is no direct formula for r, so it is found step by step, and the APR is 12 × r. Fees on the left side make the amount smaller, so r — and the APR — comes out higher than the interest rate.
Example
A $280,000 mortgage for 30 years at 6.2% has a monthly payment of $1,714.91. With $3,500 in loan fees and half a point ($1,400), you effectively borrow $275,100, while the payments stay the same. The rate that repays $275,100 with those payments is the real APR of 6.367% — about 0.17% above the interest rate.
Paying off early raises the real APR
The APR assumes you keep the loan for its full term. Most mortgages are sold or refinanced much sooner, and then the same fees are spread over fewer years. For the loan above:
| Loan kept for | Real APR |
|---|---|
| 3 years | 6.858% |
| 5 years | 6.625% |
| 10 years | 6.454% |
| 30 years (full term) | 6.367% |
If you expect to move or refinance within a few years, a loan with lower fees and a slightly higher rate can be the cheaper choice.
Fees weigh more on short loans
The same fee raises the APR much more on a short loan. A $20,000 loan at 8% with a $1,000 upfront fee:
| Term | Monthly payment | Real APR |
|---|---|---|
| 2 years | $904.55 | 13.140% |
| 3 years | $626.73 | 11.520% |
| 5 years | $405.53 | 10.196% |
| 10 years | $242.66 | 9.191% |
That is why a personal or auto loan with an origination fee can cost far more than its interest rate suggests.
APR vs. APY
APR is a nominal rate: it does not include compounding within the year. The annual percentage yield (APY), also called the effective annual rate, does, so it is a little higher. A 6% APR compounded monthly is an APY of about 6.17%. Loans are usually quoted by APR, savings accounts by APY.
How to use the APR
- compare loans by APR when they have the same amount and term but different fees;
- remember that fees weigh more on a short loan, so its APR rises faster above the interest rate;
- if you plan to sell or refinance early, look at the real APR for the years you will actually keep the loan;
- for credit cards the APR is simply the yearly interest rate — see the credit card calculator for what a balance really costs.
To see the payment and total interest of a loan without fees, use the loan calculator.