Loan Payoff Calculator

Every fixed-rate loan follows the same compounding logic: each month, interest accrues on the remaining principal, your payment covers that interest first, and whatever remains reduces the balance. Because the balance shrinks each month, an increasing share of each payment goes toward principal — this is the core of loan amortization. The payoff calculator automates this compounding process so you can see the full timeline without building a spreadsheet row by row.

The key formula used is n = −ln(1 − rP/M) / ln(1 + r), where n is the number of monthly payments, P is the current principal balance, r is the monthly interest rate (annual rate divided by 12), and M is the fixed monthly payment. This is the standard closed-form solution to the amortization equation. One critical constraint: your monthly payment must exceed the monthly interest charge (r × P); otherwise the balance grows indefinitely and the loan can never be paid off. Total interest paid is simply the total of all payments minus the original balance: (n × M) − P.

Practical applications are wide-ranging. A borrower with a $20,000 auto loan can instantly see how paying an extra $100 per month cuts years off the loan and saves hundreds in interest. Someone carrying a high-interest credit card balance can model a realistic payoff plan. Financial planners use this calculation to compare consolidation offers — if a lower interest rate reduces total interest paid even after fees, the refinance makes sense. The formula also reveals the break-even point for making extra principal payments, a powerful tool for accelerating debt freedom.

This calculator assumes a fixed interest rate and a constant monthly payment throughout the loan's life. It will not accurately model variable-rate loans where the rate adjusts periodically, or loans with changing payment schedules. The result represents the mathematical payoff point — in practice, your final payment may differ slightly from your standard monthly payment (it will typically be smaller). The calculation also does not account for fees, prepayment penalties, or interest that has already accrued and been capitalized outside the stated balance. For credit cards, the minimum payment typically changes each month as the balance decreases, meaning a fixed-payment assumption may underestimate or overestimate actual payoff time. Always verify results against your lender's amortization schedule. If the monthly payment is less than or equal to the monthly interest charge, the balance will never decrease and the calculator will return an invalid result — in this case you must increase your payment.