Time to Pay Off Loan Calculator

How to compute time-to-payoff

Under the Price (French amortization) system used by virtually every Brazilian bank, the number of installments to pay off a balance PV at monthly rate i with a fixed payment PMT is n = −ln(1 − PV·i/PMT) / ln(1 + i). The formula only converges when PMT > PV·i: if the payment is smaller than the monthly interest, the balance grows instead of shrinking and the loan becomes mathematically unpayable.

Example: R$ 20,000 at 3% per month with R$ 1,000 monthly payments. Monthly interest is R$ 600, so R$ 400 actually reduces principal. Plugging into the formula: n = −ln(1 − 0.6) / ln(1.03) ≈ 31 months. Total paid R$ 31,000, of which R$ 11,000 are interest. Doubling the payment to R$ 2,000 finishes it in 12 months and total interest drops to about R$ 3,800.

Applications in the Brazilian context

Prepaying installments triggers mandatory pro-rata interest abatement under Complementary Law 4.292/2013 (regulated by Resolution CMN 4.882/2020): banks must reduce future interest, not just shorten the schedule. Refinancing migration (portabilidade de crédito, Resolution 4.292) lets you move a loan to a cheaper lender without penalty. For consigned loans (consignado INSS/SIAPE), the legal cap of 45% of net income limits PMT and forces longer terms. Two popular debt-payoff strategies: avalanche (pay the highest-rate debt first — mathematically optimal) and snowball (pay the smallest balance first — Dave Ramsey's method, optimizes motivation by quick wins).

FAQ

Why does my balance go up if I pay less than the interest? Because unpaid interest is capitalized into the principal. Credit card revolving credit in Brazil averages above 400% per year — a R$ 1,000 minimum payment on a R$ 5,000 balance at 14% monthly barely covers interest; the debt compounds out of control.

Is the math the same for SAC (constant amortization)? No. SAC has decreasing installments and a different closed form. This calculator assumes Price (fixed PMT). For real-estate financing (Caixa, BB), SAC is more common and total interest is lower.

Does anticipating one extra payment really shorten the term that much? Yes, especially early in the loan. Each prepaid amount kills compounded future interest. On a 60-month auto loan at 1.8% per month, one extra payment in month 6 can shave 2–3 months off the schedule.

What if I refinance at a lower rate? The same formula applies with the new i. Dropping from 3% to 1.5% per month on the example above cuts payoff to roughly 23 months — a 26% time reduction. Always compare CET (Custo Efetivo Total), not just nominal rates.