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APR Calculator

See the true yearly rate of a loan (its APR) once upfront fees are counted, plus the monthly payment and the total finance charge.

Level: Grade 12 to college

  • Common Core standard HSA.SSE.B.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Printable worksheet

APR Calculator

Know the answer you need? Pick an input to work backward.

Inputs

The yearly rate the lender charges on what you owe.

Origination fees, points and other costs you pay because you borrow.

How are the fees paid?

Result

APR

8.727%

A $20,000.00 loan at 7% for 60 months with $800.00 of fees has an APR of about 8.727%.

Monthly payment
$396.02
Total finance charge (interest + fees)
$4,561.44
Total of payments
$23,761.44
Amount financed (cash received)
$19,200.00
Effective annual rate
9.085%
What the loan costs
  • Amount financed$19,200.0080.8%
  • Finance charge$4,561.4419.2%

See the step-by-step solution ↓

Step-by-step solution

  1. Count the monthly payments (n): 12 for every year of the loan

    n=5×12=60

  2. The fees come out at the start, so the cash you really get is the loan minus the fees

    received=$20,000.00−$800.00=$19,200.00

  3. Find the monthly payment at 7% interest. A standard formula gives the one amount that pays off the loan in 60 equal payments

    $20,000.00×0.005833331−(1+0.00583333)−60=$396.02

  4. Now find the monthly rate j that makes those payments worth exactly the cash you got

    $19,200.00=$396.02×1−(1+j)−60j

  5. There is no direct formula, so the calculator tries rates until both sides match

    j=0.00727274

  6. Multiply that monthly rate by 12 for a yearly rate, then by 100 for a percent. That is the APR

    APR=0.00727274×12×100=8.7273%

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: Results are estimates for planning and comparison. Lenders, banks, and tax authorities may round differently or include fees not modeled here, so confirm figures with your provider before deciding.

What this calculator does

Find out what a loan really costs you each year once its fees are counted. Two loans with the same interest rate can cost very different amounts after fees. A setup fee (often called an origination fee), discount points or a processing fee all raise what you pay to borrow. But none of them changes the interest rate written on the loan papers. The annual percentage rate, or APR, rolls those fees into one yearly rate. That lets you compare offers fairly, even when their fees are different.

Enter the loan amount, the interest rate, the term and the fees. The calculator works out your monthly payment. Then it finds the rate at which those payments exactly pay back the cash you actually received. That rate, written as a yearly figure, is the APR. You can treat the fees as paid at the start (or taken out of the loan money), or as added to what you owe.

Where it's used

Why this math matters outside the classroom:

  • Including loan fees. A $20,000, 60-month loan at 6% with a $500 fee deducted up front has an APR of about 7.06%, because only $19,500 is received.
  • Comparing offers. Borrowers compare a lower rate with high fees against a higher rate with no fees by putting both on the same APR basis.
  • Disclosure documents. Lenders compute the APR shown on loan disclosures so that loans with different fee structures can be compared.
  • Finance courses. Students solve for the rate that makes the present value of the payments equal the amount financed, using trial values.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Enter the loan amount, the interest rate the lender quotes and the term in years or months.
  2. Add up every upfront fee you pay because you're borrowing, such as origination fees and points. Enter the total.
  3. Choose how the fees are paid: up front or taken out of the loan money, or added to the loan balance.
  4. Read the APR. Then compare it with the interest rate and with the APR of other offers.

What the inputs mean

Interest rate
The yearly interest rate charged on what you owe, as stated on the loan. Lenders sometimes call it the "note" rate. The calculator divides it by 12 to get a monthly rate.
Upfront fees
Fees you pay up front because of the loan, in dollars. Lenders call these prepaid finance charges. Leave out costs you'd pay even without a loan, such as a title transfer or a home inspection.
How are the fees paid?
Paid upfront: you repay the full loan, but you only get the loan minus the fees. Added to the loan: you borrow the fees too, so the payment is higher, but you get the full amount.

Formula and method

i = rate ÷ 100 ÷ 12
payment = B × i ÷ (1 − (1 + i)^(−n))
solve for j:  received = payment × (1 − (1 + j)^(−n)) ÷ j
APR = 12 × j × 100
finance charge = payment × n − received

In the formulas, i is the monthly interest rate and n is the number of monthly payments. B is the balance the payment is based on. That's the loan amount, or the loan plus fees when you borrow the fees too. "Received" is the cash you actually get to use. That's the loan minus upfront fees, or the full loan when the fees are borrowed. j is the monthly rate the calculator solves for, and the finance charge is everything you pay minus the cash you received.

There's no exact formula that gives j directly. So the calculator closes in on it step by step. It keeps cutting the range of possible rates in half until the payments, valued in today's dollars, match the cash you received. Multiplying that monthly rate by 12 gives the APR as a stated yearly rate. That's the same method US lenders use on loan disclosures. The effective annual rate, (1 + j)^12 − 1, is also shown for reference. It counts interest earning interest within the year.

Worked example

You borrow $20,000 at 7% for 5 years and pay $800 in fees at closing.

  1. Number of payments: 5 × 12 = 60. Monthly rate: 7% ÷ 12 ≈ 0.00583333.
  2. Monthly payment on the full $20,000: about $396.02.
  3. Cash you actually receive: $20,000 − $800 = $19,200.
  4. Solve $19,200 = $396.02 × (1 − (1 + j)^−60) ÷ j, which gives j ≈ 0.00727274.
  5. APR = 0.00727274 × 12 ≈ 8.727%. Your payments total $23,761.44, so the finance charge is $4,561.44.

Result: The APR is about 8.727%, well above the 7% interest rate. If the same $800 were added to the loan instead, the payment would be about $411.86 and the APR about 8.659%.

Understanding the result

The gap between the APR and the interest rate shows how much the fees add, spread over the life of the loan. A small gap means modest fees. A large gap means the fees are a big part of what the loan costs.

Fees weigh more on short loans, because they're spread over fewer payments. The same $800 adds far more to the APR of a two-year loan than a thirty-year one. That's why APR comparisons work best between loans of the same length.

If you expect to pay the loan off early, the APR understates your real cost. You paid the fees up front, but you get fewer months of borrowing for them.

Assumptions and limitations

  • The rate is fixed, and every payment is the same amount. You pay once a month, at the end of each month.
  • All the fees you enter are paid at the start of the loan; none are charged later.
  • Every month counts as one equal period. An unusually long or short first month and daily interest aren't modeled.
  • Payments aren't rounded to the cent.
  • Which fees must be included in an official APR depends on the lender and local rules. This calculator uses whatever total you enter.
  • It doesn't handle variable-rate loans, interest-only periods, balloon payments (a large final payment) or mortgage insurance.
  • A lender's disclosure may differ slightly. That can come from rounding the payment, an unusual first period or a different set of included fees.

Frequently asked questions

Why is the APR higher than my interest rate?

Because you're paying fees on top of interest. The fees shrink the cash you really get to use, while the payments stay the same. So the true cost of borrowing goes up. With no fees, the APR equals the interest rate.

Does it matter whether fees are financed or paid upfront?

A little. Paying fees up front means you repay a loan on money you never received. Financing them (adding them to the loan) means you also pay interest on the fees, but you get the full loan amount. Both raise the APR by similar, but not identical, amounts, as the default example shows.

Is APR the same as APY?

No. APR here is a stated rate: the monthly rate times 12. APY, or the effective annual rate, also counts compounding (interest earning interest) within the year, so it's a little higher. The calculator shows the effective annual rate next to the APR.

Which fees should I include?

Include charges you pay only because you're borrowing, such as origination fees, discount points and loan processing fees. Leave out costs you'd pay anyway, like registration, sales tax or a home appraisal you'd order regardless.

How this calculator is checked

Method: Actuarial APR definition: the nominal annual rate (12 × monthly rate) at which the present value of level monthly payments equals the amount financed; solved by bisection. Payment from the standard level-payment formula. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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