APR Calculator
Convert a quoted rate plus fees into the true annual percentage rate you actually pay.
Inputs
1 point = 1% of the loan amount. Each point typically reduces the rate by ~0.25%.
Underwriting fee, flood cert, etc. Exclude title insurance, appraisal (not finance charges under TILA).
True APR
7.444%
Annual percentage rate including all prepaid finance charges (TILA definition).
Quoted Nominal Rate
7.250%
APR above Quoted Rate
0.194%
How much fees and points inflate the true rate.
Monthly Payment
$1,705.44
Total Prepaid Finance Charges
$4,750.00
Amount Financed (TILA)
$245,250.00
Points Break-Even
59months
Months needed to recoup discount points vs. taking no points.
Step by step
Monthly payment at quoted rate
PMT($250,000.00, 0.6042%, 360)
= $1,705.44
Total prepaid finance charges
$2,500 points + $1,500 origination + $0 broker + $750 other
= $4,750.00
Amount financed (TILA definition)
$250,000.00 − $4,750.00
= $245,250.00
APR is the rate where PMT(amount financed, r, n) = monthly payment.
True APR
rate($245,250.00, $1,705.44, 360) × 12
= 7.444%
0.194% above the quoted rate.
Break-even on discount points
= 59 months
If you sell or refinance before month 59, the points don't pay off.
How it works
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
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.