APR Calculator

Calculate the true Annual Percentage Rate (APR) of a loan, including closing fees.

Status: Algorithmic Audit (CPA Review Pending)
Jurisdiction: United States (IRS & SSA Standards)
Tax Year / Constants: 2026 Statutory Limits
Data Privacy: 100% Client-Side In-Browser

The Mathematical Formula

Financed Amount (Principal - Prepaid Finance Charges) = ∑ [ Monthly Payment_t / (1 + APR/12)^t ]

Variable & Parameter Definitions

  • APR The true annualized cost of credit expressed as a percentage, incorporating both note interest rate and lender prepaid fees.
  • Prepaid Finance Charges Lender origination fees, discount points, processing fees, and mandatory upfront mortgage insurance.
  • Monthly Payment_t Contractual monthly payment owed in period t; the formula solves for APR iteratively via actuarial discount.

Real-World Worked Scenario: $300,000 Loan at 6.0% Note Rate with $6,000 in Fees

A borrower takes a $300,000 30-year mortgage at a 6.0% interest rate ($1,798.65/mo) with $6,000 in upfront lender origination fees.

  1. Net Financed Loan Proceeds: $300,000 - $6,000 = $294,000.
  2. Contractual Monthly Payment: $1,798.65.
  3. Actuarial Rate Solution: Finding the internal discount rate that equates 360 payments of $1,798.65 to $294,000 net proceeds yields an APR of 6.18%.
  4. Interpretation: The 6.0% interest rate effectively costs 6.18% annually once upfront closing fees are factored in.
Key Financial Takeaway: APR reveals the true cost of borrowing. A loan with a lower interest rate but massive origination fees can have a higher APR than a zero-fee loan with a slightly higher rate.

Strategic Insights & Pitfalls to Avoid

  • ✓ Early Payoff Distortion: APR assumes you keep the loan for the full 30 years. If you sell or refinance after 5 years, the effective APR is significantly higher because upfront fees amortize over fewer years.
  • ✓ Fees Included in APR: Lender origination, points, underwriting, and processing fees are included. Title insurance and government recording fees are generally excluded.
  • ✓ Compare Apples to Apples: Use APR to compare competing lender offers with different fee structures on the exact same loan term.

Frequently Asked Questions

What is the difference between interest rate and APR?

The interest rate is the percentage charged on your principal balance. The APR includes both the interest rate and mandatory upfront lender fees, reflecting total borrowing cost.

Why is the APR almost always higher than the interest rate?

Because upfront lender fees (origination, discount points, processing) reduce your net received proceeds, raising the effective interest rate.

Can APR ever be equal to the interest rate?

Yes. If a lender charges zero points, zero origination fees, and zero prepaid finance charges, the APR equals the nominal interest rate.

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