Interest Rate Calculator

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

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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

Metric	Includes	When to Use
Interest Rate	Only interest charges	Comparing similar loan structures
APR	Interest + fees + closing costs	True 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

How do you find the interest rate on a loan from the monthly payment?

Solve the payment formula PMT = P x r / (1 - (1 + r)^-n) for r, using the amount financed, the monthly payment and the number of months. There is no algebraic solution, so it is solved by iteration (Newton-Raphson), the same method financial calculators use. Multiply the monthly rate by 12 for the annual rate.

What interest rate is $387 a month on $18,500 for 60 months?

About 9.3 percent a year. Solving the loan formula for $18,500 financed over 60 months at $387 a month gives a monthly rate of about 0.78 percent. Total payments are $23,220, so the loan costs $4,720 in interest. Use the amount financed after down payment and trade-in, not the sticker price.

Is the interest rate the same as the APR?

Not always. The rate found from principal, payment and term is the nominal interest rate. The APR can be slightly higher when the loan carries fees or closing costs that are not included in the principal. Dealers often quote only a monthly payment, so solving for the rate reveals the real cost.

Why is there no interest rate for my loan payment?

If the monthly payment times the number of months is less than the amount borrowed, no positive interest rate can produce that payment. The payments would not even repay the principal. Check that the amount entered is the amount financed and that the term is in months, not years.