Loan Payoff Calculator

This tool inverts the amortization relationship. Instead of solving for the payment given a term, it solves for the term given a payment: n = -log(1 - r x PV / PMT) / log(1 + r), where PV is the current balance, PMT the monthly payment and r the monthly rate. The expression only has a real solution when PMT exceeds r x PV, the interest accruing in the first month. Below that threshold the logarithm's argument turns negative and the balance grows without bound - the condition behind negative amortization. On a 25,000 dollar balance at 6.5 percent, first-month interest is about 135 dollars, so any payment under that amount never retires the debt. An extra payment applied to principal is worth far more than its face value because it removes that dollar from every future interest accrual. The saving on one extra dollar paid m months before the scheduled payoff is roughly (1+r)^m - 1, which is why prepayments made early dominate identical prepayments made late. Practitioners summarise the burden with the interest-to-principal ratio, total interest divided by original balance: short auto loans typically land near 8 to 15 percent, ten-year student loans near 30 to 40 percent, and thirty-year mortgages can exceed 100 percent. Two caveats matter in practice. Some servicers apply overpayments to future scheduled installments rather than to principal unless instructed otherwise, and precomputed-interest contracts plus prepayment penalties, still legal on some non-mortgage loans, can erase the benefit entirely.

Systematic early-payoff analysis grew out of two separate developments. The first was the spread of simple-interest lending. Until the 1970s many United States installment contracts were precomputed, with total finance charges fixed at signing and rebates on early payoff computed by the Rule of 78s, a sum-of-digits method that front-loaded interest and left prepaying borrowers with little refund. Consumer pressure and the Truth in Lending Act of 1968 pushed lenders toward simple-interest daily accrual, under which every extra dollar genuinely reduces future interest; Congress finally barred Rule of 78s rebates on consumer loans longer than 61 months in 1992. The second was the behavioural framing of debt repayment. The avalanche approach, paying the highest rate first, follows directly from optimisation and long predates any branding. The snowball approach, clearing the smallest balance first, was popularised by Dave Ramsey from the early 1990s onward. Research by Alexander Brown and Joanna Lahey published in 2015 and by Remi Trudel and colleagues at Boston University found that small-balance-first sequencing improves persistence even though it costs more in interest. Biweekly payment plans, which produce thirteen monthly equivalents a year, spread through mortgage servicing in the 1980s as third-party firms marketed them for a fee, a service borrowers can replicate at no cost by simply directing extra principal themselves.