Result
- Quoted nominal rate6.500%
- Upfront fees / points$4,500.00
- Net amount advancedprincipal minus upfront finance charges$245,500.00
- Payment per month$1,580.17
- Total of payments$568,861.22
- Total finance chargeinterest + fees over loan life$323,361.22
- APR − note ratefee drag on effective rate0.176%
How to use this calculator
- Enter the loan amount (the principal — what shows on the note).
- Enter the quoted interest rate (the "note rate", not an existing APR figure).
- Set the term (years) and payment frequency.
- Add all upfront finance charges — origination, discount points, prepaid finance charges. Skip property taxes, homeowners insurance, and other non-finance settlement charges per Reg Z §1026.4(c).
About this tool
Two rates show up on every loan offer and they almost never match. The "note rate" (or interest rate) is what determines your monthly payment. The APR — Annual Percentage Rate, defined by Federal Reserve Regulation Z under the Truth in Lending Act — rolls upfront finance charges (origination fees, discount points, mortgage insurance premiums on FHA loans, prepaid interest, lender title fees) back into an effective annual rate, so a 6.5% note rate with $4,500 of fees on a $250k 30-year mortgage might disclose as a ~6.66% APR. The APR is the comparison number — Reg Z explicitly designed it for shopping. This calculator runs the actuarial APR method from Reg Z Appendix J: it solves for the rate that makes the present value of all scheduled payments equal to the net amount actually advanced (principal minus upfront finance charges).
What this calculator does
Computes the effective Annual Percentage Rate for a closed-end installment loan using the actuarial method from Federal Reserve Regulation Z, Appendix J. Given the principal, quoted note rate, term, payment frequency, and upfront finance charges, the calculator solves for the rate that makes the present value of the scheduled payments equal to the net amount actually advanced — the same algorithm lenders use on the Loan Estimate and Closing Disclosure.
How it works — the formula
Period payment M = P · r / (1 − (1+r)^−n)
P = principal (note amount), r = note rate / payments per year, n = total payments
APR per Reg Z Appendix J:
Find r* such that M · (1 − (1+r*)^−n) / r* = P − upfront finance charges
Annual APR = r* × payments per yearThe note rate determines the periodic payment via the standard amortization formula. The APR then back-solves for the discount rate that makes the present value of those payments equal to the amount actually advanced — principal minus upfront finance charges. With no fees, APR equals the note rate exactly. With fees, APR exceeds the note rate, by an amount proportional to the fee fraction divided by loan duration. Reg Z Appendix J specifies an iterative actuarial method; this calculator implements a bisection solver to roughly 10⁻¹⁰ precision.
Worked examples
- Inputs:
- principal = $250,000; note rate = 6.5%; term = 30 yr monthly; upfront fees = $4,500 (1.8 points)
- Output:
- Monthly payment = $1,580.17; net advanced = $245,500; APR ≈ 6.661%; APR − rate = +0.161%
A typical 2-point pay-down on a $250k loan adds ~0.16% to the APR — meaningful only if you keep the loan past the break-even (here ~7 years).
- Inputs:
- principal = $30,000; note rate = 7.99%; term = 5 yr monthly; upfront fees = $400
- Output:
- Monthly payment = $608.27; net advanced = $29,600; APR ≈ 8.292%
A small upfront fee on a short-duration loan produces a larger relative APR bump than on a 30-year mortgage — duration matters.
- Inputs:
- principal = $50,000; note rate = 9%; term = 10 yr monthly; upfront fees = $0
- Output:
- Monthly payment = $633.38; APR = 9.000% (exact)
With zero finance charges, APR equals the note rate by definition — a useful smoke test for any APR implementation.
When to use this vs other tools
APR is the comparison number for closed-end installment credit. For other loan questions, the sibling tools below are more specific.
- Loan Calculator
You want the monthly payment, total interest, and amortization schedule from a known rate — without back-solving for APR.
- Mortgage Calculator
You want a full PITI breakdown (principal, interest, taxes, insurance) — APR covers only the finance-charge portion.
- Refinance Calculator
You want the break-even month and lifetime savings of refinancing — compare APRs at that level instead of headline rates.
- Compound Interest Calculator
You want the saving / earning side (APY-style) instead of the borrowing-cost (APR) side.
Authority note
Reg Z is the implementing regulation for the Truth in Lending Act (15 USC 1601). It defines APR, mandates disclosure on the Loan Estimate and Closing Disclosure (via TRID / Know Before You Owe), and specifies the actuarial computation method used here. CFPB took over administration from the Federal Reserve in 2011.
Limitations
- APR assumes you keep the loan to maturity. If you sell, refinance, or pay off early, the real all-in cost can be very different — particularly when discount points are involved.
- APR is only directly comparable between loans of the same type, term, and payment structure. An adjustable-rate APR uses the index-plus-margin at origination and may diverge sharply from actual payments later.
- Some "finance charges" are at the lender's discretion to classify (e.g. settlement-related fees). Compare itemized Loan Estimate Page 3 / Closing Disclosure Page 5 sections, not just the headline APR.
- This calculator handles closed-end installment credit only. Open-end credit (credit cards, HELOCs), reverse mortgages, and loans with negative amortization use different Reg Z disclosure structures.
- Reg Z permits ±0.125% tolerance for regular loans and ±0.25% for irregular loans on the disclosed APR. Small disagreements with a lender's disclosure within those bounds are expected.
APR computations are illustrative. This calculator does not provide lending, legal, or tax advice. Reg Z disclosures from your lender are the authoritative figures for any actual loan; consult the official Loan Estimate and Closing Disclosure before signing.