APR Calculator
Convert a quoted rate plus fees into the true annual percentage rate you actually pay.
About APR Calculator
APR (Annual Percentage Rate) is a federal disclosure requirement under the Truth in Lending Act (TILA). It's the interest rate that, when applied to the amount financed (the loan less all prepaid finance charges), produces the same monthly payment as the quoted rate applied to the full loan. Because prepaid charges reduce the money you actually receive while the payment stays the same, the APR is always higher than the nominal rate whenever any finance charges exist.
Formulas
Scheduled payment
Monthly payment = Loan × monthly_rate / (1 − (1+r)^−n)
- L
- Loan amount
- r
- Monthly rate = nominal_rate/12
- n
- Months
APR (TILA definition)
APR = 12 × rate where PMT(loan − finance charges, r, n) = monthly payment
- F
- Total prepaid finance charges (points + fees)
- L-F
- Amount financed
Worked example
With the default values below, APR Calculator returns True APR of 7.444%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Loan Amountaccepts 1,000–10,000,000 $
- 250,000 $
- Quoted (Nominal) Interest Rateaccepts 0–50 %
- 7.25 %
- Loan Termaccepts 1–50 years
- 30 years
- Discount Pointsaccepts 0–10 points
- 1 points
- Origination Feeaccepts 0–100,000 $
- 1,500 $
- Broker Feeaccepts 0–100,000 $
- 0 $
- Other Prepaid Finance Chargesaccepts 0–100,000 $
- 750 $
Results
- True APRAnnual percentage rate including all prepaid finance charges (TILA definition).
- 7.444%
- Quoted Nominal Rate
- 7.250%
- APR above Quoted RateHow much fees and points inflate the true rate.
- 0.194%
- Monthly Payment
- $1,705.44
- Total Prepaid Finance Charges
- $4,750.00
- Amount Financed (TILA)
- $245,250.00
- Points Break-EvenMonths needed to recoup discount points vs. taking no points.
- 59 months
Step by step
- 1Monthly payment at quoted rate= $1,705.44
- 2Total prepaid finance charges= $4,750.00
- 3Amount financed (TILA definition)= $245,250.00APR is the rate where PMT(amount financed, r, n) = monthly payment.
- 4True APR= 7.444%0.194% above the quoted rate.
- 5Break-even on discount points= 59 monthsIf you sell or refinance before month 59, the points don't pay off.
Assumptions and limits
- The result is derived only from the 7 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
- This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What's the difference between APR and interest rate?
The interest rate determines your monthly payment; APR measures the true annual cost including fees. Two lenders offering the same rate but different fees will have different APRs. Federal law requires APR disclosure precisely so borrowers can compare loans on an equal basis.
Which fees are included in APR?
Under TILA, APR must include: origination fees, discount points, broker fees, and most underwriting/processing fees. It excludes: appraisal fees, title insurance, survey costs, and government recording fees. The APR quoted on a Loan Estimate uses this precise TILA definition.
Are discount points worth it?
Points reduce your rate but cost money upfront. The break-even point is how many months of lower payments it takes to recover that upfront cost. If you sell or refinance before break-even, points were not worth it. This calculator shows the break-even assuming each point buys a 0.25% rate reduction (a common rule of thumb).
Why does a 30-year loan have a lower APR spread than a 5-year loan with the same fees?
Fees are a fixed dollar amount spread over the life of the loan. On a 30-year mortgage, that cost is amortised over 360 payments; on a 5-year loan, the same fee is spread over 60 payments, making the per-period impact — and therefore the APR inflation — larger.