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Interest Rate Calculator

Find the real interest rate on a loan from the amount, term, and monthly payment. Includes amortization schedule and payment breakdown.

$
$
years months

Total: 48 months

Interest Rate
4.620%
Interest Rate (Annual)4.620%
Monthly Rate0.380%
Total of 48 payments$30,720.00
Total interest paid$2,720.00

Payment Breakdown

Principal (91%)
Interest (9%)

How It Works

The Interest Rate Calculator determines the actual interest rate on a loan when you know three things: the loan amount, the repayment term, and the monthly payment. This is useful when a lender or car dealer quotes a payment without disclosing the rate.

The Loan Payment Formula

PMT = P × r / (1 − (1 + r)−n)

Where P is the principal, r is the monthly interest rate, and n is the number of payments. Solving for r requires iteration since there's no closed-form solution — this calculator uses the Newton-Raphson method for fast, precise results.

Common Use Cases

  • Car dealer quotes: Dealers often focus on monthly payments rather than rates — find the true rate
  • Comparing offers: Two lenders quote different terms — find which has the lower rate
  • Existing loans: Verify the interest rate on a loan you've already taken
  • Lease calculations: Estimate the implicit rate in a lease payment

Interest Rate vs APR

MetricIncludesWhen to Use
Interest RateOnly interest chargesComparing similar loan structures
APRInterest + fees + closing costsTrue cost comparison (required by law)

The rate from this calculator matches the nominal interest rate. If your loan included origination fees, points, or other costs, the effective APR will be higher.

Tips

  • Include only financed amount: Enter the loan balance after down payment, not the purchase price
  • Exclude insurance/taxes: If your payment includes escrow, insurance, or taxes, subtract those before entering the payment amount
  • Negotiate the rate, not the payment: Dealers can extend the term to lower payments while charging a higher rate — always ask for the rate

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Frequently Asked Questions

What does this calculator do?

It determines the interest rate on a loan when you know the loan amount, term, and monthly payment. Useful when a lender or dealer quotes a monthly payment but does not disclose the rate.

How is the interest rate calculated?

It uses the Newton-Raphson iterative method to solve the standard loan payment formula (PMT = P × r / (1 − (1+r)^−n)) for the rate r. This is the same method financial calculators use.

Is this the APR?

The calculated rate is the nominal interest rate based on the payment, principal, and term. The APR may be slightly higher if the loan includes fees or closing costs not reflected in the principal amount entered.

Can I use this for car loans?

Yes. Car dealers often advertise monthly payments without clearly stating the interest rate. Enter the financed amount (after down payment), loan term, and monthly payment to find the actual rate.

What if my payment is too low?

If the monthly payment multiplied by the number of months is less than the loan amount, no positive interest rate can produce that payment — the calculator will show no result.

Does this include compound interest?

Yes. The calculation assumes monthly compounding, which is standard for installment loans (auto loans, personal loans, mortgages). Each month, interest is calculated on the remaining balance.