Interest Rate Solver
Solve for the missing variable in a loan: find the interest rate, monthly payment, or loan term given the other two, plus total interest paid.
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How to use this calculator
M = monthly payment, P = principal, r = monthly interest rate, n = total months. Rearrange algebraically or iteratively to solve for the unknown variable.
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Choose what you want to solve for: interest rate, payment amount, or loan term.
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Enter the loan principal and the two known values (rate + term, or payment + term, or rate + payment).
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The calculator solves for the missing value using exact financial mathematics.
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Use the rate solver to find what APR a lender is actually charging if you know the payment and term.
Frequently asked questions
How do I find the implied rate on a car dealer offer?
Enter the car loan amount, the monthly payment the dealer quoted, and the term. Switch to "Solve for Interest Rate." The result shows the actual APR — sometimes significantly higher than what dealers imply, especially with manufacturer financing offers.
What if the payment is too low to cover interest?
This is negative amortization — the balance grows instead of shrinking. The calculator will flag this. Negative amortization products exist (some ARMs, income-based student repayment) but are risky because the outstanding balance increases over time.
How accurate is the rate solver?
The Newton-Raphson method converges to the correct rate within 10 decimal places for standard loan inputs. For unusual inputs (very high rates, very short terms) the iteration may converge slowly but will still find the correct answer within the iteration limit.
Can I use this for a balloon payment loan?
Balloon loans have a large final payment rather than uniform installments. This calculator assumes uniform payments only. For balloon loans, add the balloon amount as future value in an annuity calculator to get the correct monthly payment.
Solving for any loan variable
Why the implied interest rate matters
Dealers, retailers, and some lenders quote monthly payments without highlighting the rate. A car financed at $400/month for 72 months might look affordable, but if the implied rate is 12%, total interest is over $6,000. The interest rate solver reveals the true cost so you can compare alternatives — bank financing, credit union, manufacturer offers — on equal terms.
How loan term affects total cost
Extending a 5-year loan to 7 years on a $20,000 / 7% loan: monthly payment drops from ~$396 to ~$299, but total interest jumps from ~$3,774 to ~$5,108. The term solver helps you find the shortest term where the payment fits your budget, minimizing total interest cost.
Fixed vs adjustable: what rate should you model?
For fixed-rate loans, use the quoted rate directly. For adjustable-rate loans (ARMs), use the initial fixed rate for short planning horizons and stress-test with potential future rates using the "rate +1%" sensitivity output. A 1% rate increase on a $300,000 mortgage adds roughly $180–200 to the monthly payment.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →