Interest Rate Calculator
Solve for the unknown interest rate on a loan or investment when you know the other variables. Enter any three of the four: loan amount (present value), monthly payment, number of months, and starting or ending balance — and the calculator solves for the interest rate. Useful for figuring out the actual rate on a car loan, personal loan, or lease when the lender only shows you a payment, or for backing out the implied return on an annuity or structured settlement.
Calculator
Solve for interest rate
How the interest rate is calculated
Solving for the interest rate from payment, loan amount, and term requires iterative numerical methods because no closed-form algebraic solution exists. The calculator uses Newton-Raphson iteration: it guesses a monthly rate, computes the implied payment using the standard annuity formula, compares that to the actual payment, and adjusts the rate guess until the difference is negligible (less than $0.01). Convergence typically requires 20-50 iterations.
The relationship the calculator is solving: PV = PMT x [1 – (1 + r)^-n] / r + FV x (1 + r)^-n, where r is the monthly rate, n is the number of months, PV is the present value (loan amount), PMT is the monthly payment, and FV is the ending balance (usually zero for fully amortizing loans).
Dealers and lenders often quote monthly payments without disclosing the rate. Plug in the payment, loan amount, and term and the calculator surfaces the actual APR. A “0% financing” offer with a higher purchase price often has an implied rate — this tool makes it visible.
Balloon loans and residual values
For leases and balloon loans where a remaining balance is due at the end, enter that balance as the ending value. A car lease with a $12,000 residual after 36 months of $350 payments on a $28,000 vehicle, for example, implies a rate you can back out with this calculator. Manufacturers sometimes subsidize lease rates below market to move inventory — the implied rate on a lease can be 0-2% or negative if the manufacturer is absorbing the cost.