APR Calculator
Calculate the true Annual Percentage Rate (APR) on any loan. See how origination fees, discount points, and closing costs increase your actual borrowing cost beyond the stated interest rate.
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APR (Annual Percentage Rate)
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Monthly Payment —
Total Interest + Fees —
Total Cost of Loan —
APR vs Stated Rate Difference —
Extended More scenarios, charts & detailed breakdown ▾
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True APR
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Monthly Payment —
Total Fees —
APR Premium over Rate —
Professional Full parameters & maximum detail ▾
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Rate Comparison
True APR (Newton-Raphson) —
Stated Rate —
APR vs Stated Rate —
Dollar Cost of APR Spread —
Payment Details
Monthly Payment (P&I) —
Total Financed Fees —
Total Interest —
Total Loan Cost —
How to Use This Calculator
- Enter your Loan Amount, stated Interest Rate, and Loan Term in months.
- Add all known fees in the Total Fees & Costs field.
- The calculator returns the true APR using bisection method.
- Use the Mortgage APR tab for mortgage-specific inputs (points, closing costs, prepaid interest).
- Use the Professional tier for full Newton-Raphson APR with PMI and itemized fees.
Formula
APR is derived by finding the monthly rate r such that: Loan Proceeds = Σ Payment / (1+r)^k for k=1 to n
Then: APR = r × 12 × 100
Loan Proceeds = Loan Amount − All Upfront Fees
Monthly Payment uses the stated rate, not APR.
Then: APR = r × 12 × 100
Loan Proceeds = Loan Amount − All Upfront Fees
Monthly Payment uses the stated rate, not APR.
Example
Example: $20,000 loan at 6.5% for 60 months with $500 fees.
Monthly payment (at 6.5%): $391.32
Net proceeds to borrower: $19,500
True APR ≈ 7.06% — about 0.56% higher than the stated rate.
Monthly payment (at 6.5%): $391.32
Net proceeds to borrower: $19,500
True APR ≈ 7.06% — about 0.56% higher than the stated rate.
Frequently Asked Questions
- APR (Annual Percentage Rate) is the true annual cost of borrowing, including all fees and costs spread over the life of the loan. It is always equal to or higher than the stated interest rate. Use APR to compare loans with different fee structures apples-to-apples.
- The stated interest rate only reflects the cost of the principal. APR adds origination fees, discount points, prepaid interest, and certain closing costs. On a $20,000 loan with a 6.5% rate and $500 in fees, the APR is closer to 7.0%.
- Under the Truth in Lending Act (TILA), APR must include: origination fees, discount points, prepaid interest, and certain broker fees. It generally excludes title insurance, appraisal, and most closing cost line items for mortgages.
- The Professional tab uses Newton-Raphson iteration — a numerical root-finding algorithm that converges to the precise monthly rate where the present value of all loan payments equals the net loan proceeds (after fees). This is the most accurate APR calculation method.
Related Calculators
Sources & References (5) ▾
- CFPB — What is APR? — Consumer Financial Protection Bureau
- Truth in Lending Act (Regulation Z) — APR Requirements — Consumer Financial Protection Bureau
- Federal Reserve — Consumer Credit Rates — Federal Reserve
- FTC — Understanding Loan Costs — Federal Trade Commission
- FDIC — APR and Finance Charges Explained — Federal Deposit Insurance Corporation