How to use the apr calculator
- Enter the loan amount, the one printed on the offer before fees are taken out.
- Choose what you know: the interest rate or the monthly payment. With a rate, the payment is worked out. With a payment, the rate that produces it is solved for.
- Enter the term in years and months, then the origination fee or points as a percent of the loan and any other upfront fees in dollars.
- Read the APR, the gap above the interest rate, the totals, and the table that shows the APR if you repay the loan early.
Formula
Amount received = loan amount - upfront fees
Payment = L x i / (1 - (1 + i)^-n)
Find the monthly rate i such that payment x (1 - (1 + i)^-n) / i = amount received
APR = 12 x i
This is the actuarial method used for equal monthly payments: the APR is the interest rate that makes the payments worth exactly what you received. The equation has no closed-form answer, so it is solved by bisection and then checked by discounting every payment one by one.
Worked example
A $20,000 loan at an 8% rate over 5 years has a monthly payment of $405.53. A 3% origination fee is $600, so you receive $19,400.
The payments add up to $24,331.80, so interest and fees together are $4,931.80. The monthly rate that makes 60 payments of $405.53 worth $19,400 is about 0.7749%, which gives an APR of 9.299%, 1.299 points above the 8% rate.
If you repay after 1 year, the balance is $16,611.17 and the same fee is spread over only 12 months, so the APR is 11.448%. After 2 years it is 9.974%, and after 3 years 9.526%.
Interest rate versus APR
The interest rate sets the interest charged on the balance. The APR folds in certain upfront charges so that two offers can be compared on one scale. A loan with a lower rate but a large origination fee can cost more than a loan with a slightly higher rate and no fee, and the APR is designed to expose that. The Consumer Financial Protection Bureau explains that an APR reflects the interest rate plus other charges.
APR is still only one measure. It assumes you keep the loan to the end of the term, which is why the early repayment table is included. If you expect to sell or refinance sooner, the shorter horizon figures are the better guide to what the fees really cost you.
Which fees to include
Include fees that your lender counts as part of the cost of credit, such as origination fees, discount points and processing fees. Fees for services you would pay anyway, such as an appraisal on some mortgages, may be treated differently in the official APR, so check your Loan Estimate or loan agreement line by line.
This tool cannot know how a lender classifies each charge. That is why it is an estimate. For loans where points are a choice, the mortgage points calculator shows when paying points breaks even, and the interest rate calculator finds a rate from a payment and term.
How accurate is the result
The math follows the actuarial method for equal monthly payments, with the first payment one month after funding. Real loans can have odd first periods, daily interest accrual, variable rates and other features that change the legal APR slightly. The APR on your disclosure is the figure that governs, and this page is not a Truth in Lending disclosure.
Because the payment is rounded to the cent, a loan with no fees can show an APR a hair above the rate, for example 8.0002% shown as 8%. That is a rounding effect, not a hidden cost.
Assumptions and limits
- Payments are equal and monthly, and the first payment is exactly one month after the loan funds.
- Interest accrues monthly at the rate divided by 12. Daily accrual, odd first periods and variable rates are not modeled.
- All upfront fees you enter are treated as paid at closing, either from the loan proceeds or in cash. Both reduce what you effectively receive.
- The early repayment table assumes you pay the exact remaining balance with no prepayment charge.
- The result is an estimate. It is not a Truth in Lending disclosure, and the APR on your loan documents governs.
- Insurance products, taxes and charges that your lender does not count in its APR are not included.
Frequently asked questions
How is APR calculated with fees?
Subtract the upfront fees from the loan amount to get what you actually receive, then find the monthly rate at which your payments are worth exactly that amount. Twelve times that rate is the APR. With the example loan, fees lift 8% to 9.299%.
Why is my APR higher than my interest rate?
Because you pay interest on the full loan but receive less than the full loan after fees. The gap between what you received and what you repay is larger than interest alone would produce, so the effective yearly cost is higher.
Does paying a loan off early change the APR?
Yes. Fees are a fixed cost, so when the loan ends sooner they are spread over fewer months and the effective yearly cost rises. In the example, repaying after one year turns a 9.299% APR into 11.448%.
Can I find the APR if I only know the monthly payment?
Yes. Choose Monthly payment, and the tool first solves for the interest rate that your payment, amount and term imply, then finds the APR after your fees. A $405 payment on the example loan implies a rate of 7.945%.
Is this the APR my lender will quote?
It should be close for a simple loan with equal monthly payments, but lenders follow detailed rules on which charges count and how periods are measured. Use the figure on your official disclosure when they differ.