Payment Calculator Formula & How It Works
n = −ln(1 − (P×r)/M) ÷ ln(1+r) (solve for term)
- n = Number of payments (solve for if unknown)
- r = Monthly rate (solve for if unknown using Newton-Raphson)
- P = Loan principal
- M = Known monthly payment
When you know your monthly payment and loan amount, you can solve for the unknown: either how many payments remain, or the implied interest rate. Solving for n is straightforward. Solving for r requires iterative numerical methods (Newton-Raphson). This helps understand the true cost of buy-now-pay-later and deferred interest offers.