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Find implied interest rate from loan amount, payment and term — solve for APR.
Find implied interest rate from loan amount, payment and term — solve for APR.
Enter values above and click Calculate — results will appear here with the formula explained.
This calculator inverts the standard amortizing loan formula to solve for the implied annual rate when you already know loan amount, monthly payment and term. Because the rate is trapped inside both the numerator and the exponent, there is no closed-form inverse — so the implementation binary-searches between 0% and 50% APR until the payment that rate produces matches your payment within a cent.
Convergence is typically within 0.01 percentage point, which is enough to verify a lender's quoted APR, compare a dealer's financing against a bank pre-approval, or decide whether refinancing actually moves the rate as much as the salesperson claims. The result assumes a fixed rate, monthly compounding, and no fees; origination points or variable-rate adjustments must be compared separately.
Find implied interest rate from loan amount, payment and term — solve for APR. Formula: Solve r in payment = P*r*(1+r)^n/((1+r)^n-1) via binary search. Example: With $25k loan, $500/mo for 60 months, implied rate about 7.4% APR.
This calculator inverts the standard amortizing loan formula to solve for the implied annual rate when you already know loan amount, monthly payment and term. Because the rate is trapped inside both the numerator and the exponent, there is no closed-form inverse — so the implementation binary-searches between 0% and 50% APR until the payment that rate produces matches your payment within a cent.
Convergence is typically within 0.01 percentage point, which is enough to verify a lender's quoted APR, compare a dealer's financing against a bank pre-approval, or decide whether refinancing actually moves the rate as much as the salesperson claims. The result assumes a fixed rate, monthly compounding, and no fees; origination points or variable-rate adjustments must be compared separately.
With $25k loan, $500/mo for 60 months, implied rate about 7.4% APR.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
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