Estimate the fee-inclusive APR of a loan — a modeled annualized cost after entered fees, not just the interest rate. The general tab handles any installment loan with compounding and pay-back options; the mortgage tab is the US monthly case with points and PMI.
What typically goes into a US mortgage APR
| Usually included | Usually excluded |
|---|---|
| Origination and underwriting fees | Appraisal and survey fees |
| Discount / origination points | Title insurance |
| Mortgage-broker and processing fees | Prepaid taxes and insurance in escrow |
| PMI (while required) | Builder warranties |
Examples
General: $100,000 · 6% · 10 years · $2,500 upfront
Monthly compounding and monthly payments produce a $1,110.21 payment. You repay $133,224.60 over 120 months ($33,224.60 interest). Adding the $2,500 closing fee, the estimated fee-inclusive APR is 6.563%.
Mortgage: $350,000 house · 20% down · 6.2% · 30 years
The $280,000 loan pays $1,714.91 a month. $3,500 of fees plus 0.5 points raise the estimated fee-inclusive APR to 6.367%. All payments and fees total $620,868.73.
Formula
The contractual payment amortizes the amount financed at the note rate. For a
periodic rate r over n payments:
payment = P × r / (1 − (1 + r)^(−n))
r comes from the compounding / pay-back maps (n = (years + months/12) × ppy;
daily uses a 365.25-day year):
discrete: r = (1 + i/m)^(m/ppy) − 1
continuous: r = exp(i/ppy) − 1
Loaned fees are added to P. Totals are round(payment × n, 2). Estimated fee-inclusive APR is
the IRR of the (cent-rounded) payment series against cash to the borrower
(loan − upfront fees, not amount financed minus fees), then:
APR = round(12 × ((1 + r_irr)^(ppy/12) − 1) × 100, 3)
Mortgage PMI, when down is under 20%, is an extra monthly cash flow until remaining LTV drops to 80% of the house value.
Disclosure limits
The result is a cash-flow estimate, not a lender's Truth in Lending disclosure. Legal APR calculations can depend on which charges are finance charges, exact payment and disbursement dates, rounding, irregular first periods, and product-specific rules. The CFPB explains the difference between interest rate and APR. Use the lender's official Loan Estimate or credit agreement for comparison and closing decisions.