Interest Rate Calculator

Determine the implied interest rate on a loan given the loan amount, monthly payment, and loan term. Useful for understanding the true cost of financing.

Loan Details

$
$
yrs

Enter your loan details and click "Calculate" to find the implied interest rate.

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Pro Tip

If a dealer or lender quotes you a monthly payment but not the rate, use this calculator to find the hidden interest rate. You may discover the rate is much higher than you expected.

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Understanding Interest Rates

The interest rate is the cost of borrowing money, expressed as a percentage of the loan amount. It determines how much extra you pay on top of the principal over the life of the loan. Even small differences in interest rates can have a significant impact on the total cost of a mortgage or loan.

When you know your loan amount, monthly payment, and term length but not the interest rate, you can reverse-engineer the rate. This is common when evaluating dealer financing offers, seller-financed real estate, or any situation where the rate is not explicitly stated but the payment amount is given.

Unlike most loan calculations that have direct formulas, finding the interest rate from the payment amount requires an iterative numerical approach. This calculator uses Newton's method, a fast and reliable algorithm, to solve for the rate that produces the exact monthly payment you enter.

The relationship between interest rate and monthly payment is nonlinear. Doubling the rate does not double the payment. At low rates, much of your payment goes toward principal. At higher rates, a larger share goes toward interest, meaning less of each payment reduces your balance.

Loan Payment Formula (solved for rate)

M = P × r / (1 − (1 + r)−n)

Where:

M = Monthly payment

P = Principal (loan amount)

r = Monthly interest rate (annual rate / 12)

n = Total number of monthly payments (years x 12)

Example

$250,000 loan with $1,500/month payment over 30 years:

  • • Given: P = $250,000, M = $1,500, n = 360 months
  • • Solve iteratively for r using Newton's method
  • • Result: r = 0.3876% monthly = 4.65% annual
  • • Total paid: $1,500 x 360 = $540,000
  • • Total interest: $540,000 - $250,000 = $290,000

Frequently Asked Questions

Why can't the interest rate be calculated with a simple formula?
The standard loan payment formula relates payment, principal, rate, and term. While you can easily solve for payment given the other three values, solving for the rate requires finding the root of a nonlinear equation. There is no algebraic closed-form solution, so numerical methods like Newton's method or bisection are used instead.
How accurate is this calculator?
This calculator uses Newton's method with a bisection fallback, iterating until the result converges to within a tiny tolerance. The calculated rate is accurate to many decimal places and produces a monthly payment that matches your input to within a fraction of a cent.
What is the difference between interest rate and APR?
The interest rate is the base cost of borrowing. The APR (Annual Percentage Rate) includes the interest rate plus other costs such as origination fees, closing costs, and mortgage insurance. APR gives a more complete picture of the total borrowing cost and is typically higher than the nominal interest rate.
Can I use this for any type of loan?
Yes. This calculator works for any fixed-rate, fully amortizing loan with equal monthly payments, including mortgages, auto loans, personal loans, and student loans. It does not apply to interest-only loans, adjustable-rate loans, or loans with irregular payment schedules.