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What is the APR of my loan?

Enter the loan amount, the interest rate, the number of monthly payments and the upfront fees to see the loan's APR, monthly payment and finance charge.

Your numbers

For example 60 for 5 years, 360 for 30 years.
Origination fee, points, other lender charges.
APR
7.274%

A $25,000.00 loan at 6% for 60 months with $750.00 of fees has an APR of 7.274% and a monthly payment of $483.32.

Monthly payment
$483.32
Amount financed
$24,250.00
Finance charge
$4,749.20
Total interest
$3,999.20
Total of payments
$28,999.20

APR: 7.274%. A $25,000.00 loan at 6% for 60 months with $750.00 of fees has an APR of 7.274% and a monthly payment of $483.32.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

Computes the annual percentage rate (APR) of a fixed-rate loan with monthly payments from the loan amount, interest rate, term and upfront fees, by the Regulation Z actuarial method.

Example with the default inputs (Loan amount $25,000.00, Interest rate 6%, Loan term (months) 60, Upfront fees $750.00, Add the fees to the loan No): A $25,000.00 loan at 6% for 60 months with $750.00 of fees has an APR of 7.274% and a monthly payment of $483.32.

Method: Payment = PMT(borrowed, rate ÷ 12, months). APR = 12 × j, where j is the monthly rate at which the payments’ present value, payment × (1 − (1 + j)^−n) ÷ j, equals the amount financed (loan amount minus upfront fees).

  • A fixed-rate loan with equal monthly payments, the first one month after the loan starts (no odd first period).
  • Upfront fees are prepaid finance charges: they lower the amount financed whether you pay them in cash or add them to the loan.
  • The APR is the Regulation Z actuarial APR: the monthly rate × 12, with no compounding into a yearly rate.
  • Fees that are not finance charges (for example some title or appraisal fees on a mortgage) should be left out.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Loan amount $20,000.00, Interest rate 5%, Loan term (months) 60, Upfront fees $500.00, Add the fees to the loan no gives APR 6.047963%, Monthly payment $377.42, Amount financed $19,500.00, Finance charge $3,145.48, Total interest $2,645.48.Source: Regulation Z appendix J actuarial method (APR = 12 × the monthly rate at which 60 payments of $377.42 are worth $19,500); hand calculation in content.mdx; Python bisection
  2. Loan amount $20,000.00, Interest rate 5%, Loan term (months) 60, Upfront fees $500.00, Add the fees to the loan yes gives APR 6.02196%, Monthly payment $386.86, Amount financed $20,000.00.Source: Regulation Z appendix J actuarial method with $20,500 borrowed and $20,000 financed; Python bisection
  3. Loan amount $25,000.00, Interest rate 6.5%, Loan term (months) 72, Upfront fees $0.00, Add the fees to the loan no gives APR 6.5%, Monthly payment $420.25.Source: Regulation Z: with no finance charge but interest, the APR equals the interest rate; hand calculation in content.mdx
  4. Loan amount $12,000.00, Interest rate 0%, Loan term (months) 36, Upfront fees $300.00, Add the fees to the loan no gives APR 1.649977%, Monthly payment $333.33, Finance charge $300.00.Source: Regulation Z appendix J: a 0% loan with a $300 fee; 36 payments of $333.33 are worth $11,700 at 1.65% APR (Python bisection)

How the APR is worked out

  1. Borrowed. The loan amount, plus the fees if you add them to the loan.
  2. Amount financed. The credit you actually get: the loan amount minus the fees when you pay them up front, or the loan amount when the fees are added on. Either way it is the amount borrowed minus the fees.
  3. Monthly payment at the interest rate r (yearly, in percent) over n months: payment = B × i ÷ (1 − (1 + i)^−n), where B is the amount borrowed and i = r ÷ 1,200. At 0% it is B ÷ n.
  4. APR. Find the monthly rate j at which the payments are worth the amount financed: amount financed = payment × (1 − (1 + j)^−n) ÷ j. Then APR = 12 × j, in percent. This is the actuarial method of Regulation Z, appendix J, with a monthly unit period. There is no simple formula for j, so the calculator finds it by bisection on j ≥ 0 (the present value falls as j rises), computing (1 + j)^−n as e^(−n × ln(1 + j)) so very high rates stay exact.

The calculator also shows:

  • total of payments = payment × n
  • total interest = total of payments − amount borrowed
  • finance charge = total of payments − amount financed (all the interest plus the fees)

Assumptions

  • A fixed rate and equal monthly payments, the first one month after the loan starts.
  • The fees you enter are finance charges paid when the loan starts. Leave out fees that are not finance charges.
  • There is no answer when you pay the fees up front and they are as large as the loan amount.

Worked examples by hand

$20,000 at 5% for 60 months, $500 of fees paid up front. i = 5 ÷ 1,200 = 0.0041667. Payment = 20,000 × 0.0041667 ÷ (1 − 1.0041667^−60) = $377.42. Amount financed = 20,000 − 500 = $19,500. Total of payments = 377.42 × 60 = $22,645.48, so total interest is $2,645.48 and the finance charge is $3,145.48. The monthly rate at which 60 payments of $377.42 are worth $19,500 is 0.50400%, so the APR = 12 × 0.50400% = 6.048%.

The same loan with the fees added on. Borrowed = $20,500, payment = $386.86, amount financed = $20,000. APR = 6.022%.

$25,000 at 6.5% for 72 months, no fees. The amount financed is the full $25,000, so the payments are worth $25,000 at the interest rate itself: APR = 6.5%. Payment = $420.25.

$12,000 at 0% for 36 months with a $300 fee. Payment = 12,000 ÷ 36 = $333.33. Amount financed = $11,700. Finance charge = 12,000 − 11,700 = $300. The monthly rate at which 36 payments of $333.33 are worth $11,700 gives an APR of 1.650%.

Other questions people ask

What is the difference between the interest rate and the APR?

The interest rate is what the lender charges on the money you borrow. The APR is the yearly cost of the credit including upfront finance charges such as origination fees and points. With no fees the two are equal; fees push the APR above the interest rate.

How is APR calculated?

First the monthly payment is worked out at the interest rate. The APR is then the yearly rate at which those payments exactly repay the amount financed: the loan amount minus the upfront fees. Regulation Z calls this the actuarial method; the monthly rate is multiplied by 12.

What does $500 of fees do to a 5% car loan?

On $20,000 over 60 months at 5%, the payment is $377.42. You get $19,500 of credit after the fees, so the APR is the rate at which 60 payments of $377.42 repay $19,500: 6.05%.

Which fees count in the APR?

Finance charges: fees you pay because you take the credit, such as origination fees, points, and many lender service charges. Fees you would pay in a cash deal, and some real estate fees such as title and appraisal fees, are not finance charges. Ask the lender for the Truth in Lending disclosure to see which fees they counted.

Is it better to pay fees up front or add them to the loan?

Adding fees to the loan means you pay interest on them, so the finance charge is higher, but the APR is similar, because both count the fees as a cost of credit. $500 of fees on $20,000 at 5% for 60 months gives an APR of 6.05% paid up front and 6.02% added to the loan.

How accurate does a lender's APR have to be?

For a regular loan, Regulation Z treats a disclosed APR as accurate if it is within 1/8 of a percentage point of the actuarial APR.