Loan Rate โ Find Your True APR
Calculate annual interest rate from payment, principal, and term. Verify lender quotes and compare to market rates.
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APR includes feesโcompare APR when shopping Newton-Raphson iteratively solves the amortization equation Market rates vary by loan type and credit Add origination fees for true cost
Ready to run the numbers?
Why: Knowing your true APR helps you compare loan offers and verify lender quotes. Fees can hide the real cost.
How: Enter loan amount, payment, term, and optional fees. Uses Newton-Raphson to solve for the rate.
Run the calculator when you are ready.
Loan Rate Calculator โ Find Your True APR
Calculate annual interest rate from payment, principal, and term. Verify lender quotes and compare to market rates.
Sample Scenarios โ Click to Load
Loan Information
Principal, Interest, Fees breakdown
10.4% of total cost is interest
Market Rate Comparison
| Loan Type | Market Rate | Your Rate | Difference |
|---|---|---|---|
| Auto Loan (New) | 5.50% | 1200.00% | +1194.50% |
| Auto Loan (Used) | 7.20% | 1200.00% | +1192.80% |
| Personal Loan (Excellent) | 6.50% | 1200.00% | +1193.50% |
| Personal Loan (Good) | 9.50% | 1200.00% | +1190.50% |
| Personal Loan (Fair) | 14.50% | 1200.00% | +1185.50% |
| Student Loan (Federal) | 5.50% | 1200.00% | +1194.50% |
| Student Loan (Private) | 7.80% | 1200.00% | +1192.20% |
| Mortgage (30-Year) | 6.80% | 1200.00% | +1193.20% |
| Mortgage (15-Year) | 6.20% | 1200.00% | +1193.80% |
| Business Loan (SBA) | 8.50% | 1200.00% | +1191.50% |
| Credit Card (Avg) | 24.50% | 1200.00% | +1175.50% |
Calculation Breakdown
Input Values
Rate Calculation
Cost Summary
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1. Key Takeaways
- โข APR is the true annual cost including fees; stated rate may exclude them
- โข Newton-Raphson method solves for rate when payment, principal, term are known
- โข Verify lender quotes โ payment-based offers often hide the real rate
- โข Compare to market rates to see if you're getting a fair deal
- โข Fees (origination, points) increase effective rate even if nominal rate is low
- โข EAR (effective annual rate) reflects compounding; higher than APR for monthly compounding
2. Did You Know?
Newton-Raphson
Iterative method to solve for rate when PMT, P, n are known
APR vs Stated
APR includes fees; stated rate often excludes origination
Market Comparison
Auto 7-9%, mortgage 6-8%, personal 10-25% typical
EAR vs APR
EAR = (1+r/12)^12 - 1 for monthly compounding
Fee Impact
1% origination on $30K = $300 added to cost
Shop 3-5 Lenders
Rates vary widely; compare before signing
3. How Loan Rate Is Calculated
Given principal (P), payment (PMT), and term (n), the rate (r) is solved iteratively using Newton-Raphson. PMT = P ร r(1+r)โฟ / ((1+r)โฟ - 1). Fees are added to cost for true APR.
Inputs
Principal, payment, term, fees
Outputs
APR, EAR, total interest, market comparison
4. Expert Tips
Include all fees
Origination, points โ for true APR
Shop 3-5 lenders
Rates vary widely; compare APR to APR
Verify lender quotes
Payment-based offers often hide real rate
Autopay discount
Many offer 0.25-0.5% off for autopay
5. Typical Market Rates (Jan 2026)
| Loan Type | Typical APR |
|---|---|
| Auto (new) | 7-9% |
| Mortgage (30yr) | 6-8% |
| Personal | 10-25% |
6. FAQ
APR includes fees; stated rate often excludes them. APR is the true cost.
Newton-Raphson is highly accurate (within 0.0001%). Same method used by banks.
Effective Annual Rate accounts for compounding. Slightly higher than APR for monthly.
Credit score, loan type, lender, term, and market conditions affect your rate.
Yes. Origination, points, and other fees increase effective APR.
Always compare APR to APR. Different lenders quote different rate types.
7. Quick Stats
0.0001%
Newton-Raphson accuracy
3-5
Lenders to shop
0.25-0.5%
Autopay discount
APR
True cost includes fees
8. Sources
9. Disclaimer
โ ๏ธ Warning: This calculator provides estimates. Market rates are approximate. Include all fees for true APR. Not financial advice.
For educational purposes only โ not financial advice. Consult a qualified advisor before making decisions.
๐ก Money Facts
APR is the annual rate that makes payment ร term = principal + interest + fees.
โ Finance
Newton-Raphson converges to the rate in a few iterations.
โ Math
Auto loans: 5-10%. Personal: 8-24%. Mortgage: 6-8%.
โ Market
Always include fees for true cost comparison.
โ CFPB
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