What the APR represents
Fees change what a loan really costs. If you borrow $20,000 but pay a $600 fee to get it, you walk away with $19,400 while still making payments sized for $20,000. The APR is the interest rate at which $19,400 would produce exactly those payments. It folds the fee into one comparable number, so a 6.5% loan with high fees can turn out more expensive than a 6.75% loan with none.
The method
Payment PMT = L × i / (1 − (1 + i)^−n), i = note rate / 12, L = amount + financed fees Amount financed AF = loan amount − fees paid at closing APR = 12 × j, where j solves AF = PMT × (1 − (1 + j)^−n) / j
There is no closed-form answer for j, so the calculator solves for it numerically (bisection to well beyond the 1/8 of a percentage point accuracy Regulation Z requires for regular loans).
Worked examples
$20,000 at 7% for 60 months with a $600 origination fee: the payment is $396.02, the amount financed is $19,400, and the rate that discounts 60 payments of $396.02 back to $19,400 is 0.6905% a month — an APR of 8.29%.
A $200,000 30-year mortgage at 6% with 2 points ($4,000) paid at closing: payment $1,199.10, amount financed $196,000, APR 6.19%.
Limitations
- For regular fixed-rate, fixed-payment loans with the first payment one month after closing. Odd first periods, adjustable rates, mortgage insurance and balloon payments change a lender's APR.
- Which fees count as finance charges is a legal question; this calculator uses whatever fees you enter.
- APR is shown to two decimals.
Sources: Consumer Financial Protection Bureau, Regulation Z §1026.22, Determination of annual percentage rate, and §1026.4, Finance charge; CFPB, Interest rate vs. APR.
Frequently asked questions
What is the difference between the interest rate and the APR?
The interest rate sets your monthly payment. The APR is the yearly cost of the credit once certain fees are counted too, expressed as a single rate. Two loans with the same 6% rate but different fees have different APRs, which is why lenders must disclose APR under the Truth in Lending Act.
Which fees go into the APR?
Finance charges: fees you pay as a condition of getting the credit, such as origination fees, discount points, mortgage broker fees and prepaid interest. Costs you would pay in a cash deal — title insurance, appraisal, credit report and recording fees on a mortgage — are generally excluded. Regulation Z, 12 CFR 1026.4, has the full list.
Does it matter whether fees are paid up front or financed?
For the APR, either way the fee is a finance charge. If you pay it at closing, you borrow the full amount but receive less cash. If you roll it into the loan, the payment rises. This calculator handles both: "Fees paid at closing" reduce the amount financed; "Fees added to the loan" increase the amount borrowed.
Why is APR higher on a shorter loan with the same fees?
Fees are spread over fewer years, so they add more per year. A $600 fee on a $20,000 loan at 7% raises the APR to about 8.29% over 5 years but to about 9.07% over 3 years.
Is APR the same as APY?
No. APY (annual percentage yield) includes compounding and is used for savings. APR on a loan is the periodic rate times the number of periods in a year, without compounding — 12 × the monthly rate.
CalcNest results are estimates based on the inputs and assumptions above, not financial, tax or lending advice. A lender's official Loan Estimate or your account statement is the final word.