Interest Rate Calculator

Calculate the implied interest rate (APR) from a loan principal, monthly payment, and term. Compare multiple loan offers, find the rate from total paid, and analyze nominal vs effective rates with fee impact.

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Implied APR
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Total Interest Paid —
Extended More scenarios, charts & detailed breakdown ▾
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Implied APR
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Monthly Rate —
Total Interest —
Professional Full parameters & maximum detail ▾
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Rate Analysis

Nominal APR (Implied) —
Effective APR (with Fees) —
Effective Annual Rate (EAR) —
Real Rate After Inflation —

Cost Summary

Total Interest Paid —
Total Cost Including Fees —

How to Use This Calculator

  1. Enter your loan principal, monthly payment, and term in months to instantly calculate the implied APR.
  2. Use the Find Rate from Payment tab for a detailed rate breakdown including monthly rate.
  3. Use the Find Rate from Total Paid tab when you know what you paid in total (e.g., from a payoff statement).
  4. Use the Compare Offers tab to calculate and compare monthly payments for 3 different APR offers.
  5. Use the Professional tab for nominal APR, effective APR with fees, EAR at any compounding frequency, and real rate after inflation.

Formula

Implied APR: solve P = PMT × (1 − (1+r)^-n) / r for r, then APR = r × 12
EAR = (1 + APR/periods)^periods − 1
Real Rate = (1 + APR) / (1 + Inflation) − 1

Example

Example: $20,000 loan, $400/month payment, 60 months. Total paid = $24,000. Total interest = $4,000. Implied APR ≈ 7.42%. EAR (monthly compounding) ≈ 7.69%.

Frequently Asked Questions

  • If you know your loan amount, monthly payment, and term, you can back-solve for the interest rate using a numeric method (bisection or Newton-Raphson). Our calculator does this automatically — just enter your principal, monthly payment, and number of months to find the implied APR.
  • The stated interest rate is the base cost of borrowing. APR (Annual Percentage Rate) includes fees, points, and other costs, making it the true cost of the loan. A loan with a 6% interest rate and $500 origination fee will have a higher effective APR than 6%, especially on shorter-term loans.
  • The EAR accounts for compounding frequency. A 12% APR compounded monthly has an EAR of 12.68% because interest compounds each month. The EAR is always higher than the nominal rate unless compounding is annual.
  • The real interest rate = ((1 + nominal rate) / (1 + inflation rate)) − 1. If your loan is at 7% and inflation is 3%, the real cost of borrowing is approximately 3.88%. For fixed-rate debt, inflation benefits borrowers since they repay in cheaper future dollars.

Related Calculators

📊 APR Calculator 💰 Loan Calculator 📋 Amortization Calculator 📈 Compound Interest Calculator
Sources & References (5) ▾
  1. Federal Reserve — Selected Interest Rates (H.15) — Federal Reserve
  2. CFPB — Interest Rate vs. APR — Consumer Financial Protection Bureau
  3. Federal Reserve — Federal Funds Rate and Monetary Policy — Federal Reserve
  4. FDIC — Interest Rate Risk Management — Federal Deposit Insurance Corporation
  5. Truth in Lending Act (Regulation Z) — APR Requirements — Consumer Financial Protection Bureau