PMT Loan Payment Calculator

How the PMT formula works

PMT is the fixed installment of an amortizing loan under the French (Tabela Price) system: PMT = PV · i / (1 − (1 + i)^(−n)), where PV is the present value (loan principal), i is the interest rate per period (as a decimal), and n is the number of installments. The payment stays constant; interest dominates the first installments and amortization grows over time. The SAC system (constant amortization) is different: amortization is fixed at PV / n and each installment is PMT_k = Amort + (PV − Amort · (k − 1)) · i, so payments decrease over time.

Concrete example: a R$ 50,000 loan at 1% per month over 60 months. Tabela Price gives PMT ≈ R$ 1,112 fixed; SAC starts at about R$ 1,333 and falls roughly R$ 8 per month. The total interest paid under SAC is lower because the principal is amortized faster. In Brazil, the effective cost (CET — Custo Efetivo Total) must include the contractual rate plus insurance, registration fees, and IOF (4.38% per year capped at 3 years, plus a 0.38% flat on disbursement). Always compare CETs across lenders, not headline rates.

Where PMT is used

Vehicle financing (CDC), mortgages under SFH and SFI, equipment leasing, working-capital loans, BNDES credit lines, and consumer credit in general. Outside Brazil, every fixed-rate mortgage and auto loan in the US uses the same formula. Spreadsheets call it =PMT(rate, nper, pv) in Excel/Google Sheets — same math.

FAQ

Why does the bank quote a monthly rate but charge me yearly equivalent differently? A 1% monthly rate compounds to (1.01)^12 − 1 = 12.68% effective per year, not 12%. Be sure to convert with the equivalent rate formula, not by multiplying by 12 (that gives the nominal rate).

Price or SAC: which is cheaper? SAC pays less total interest because principal is amortized faster, but the first installments are heavier — you need higher income to qualify. Price keeps installments flat, which fits tight budgets but costs more in total.

What does CET include? Interest rate, insurance (MIP and DFI for mortgages), registration and administrative fees, and IOF for non-mortgage credit. Two loans with the same headline rate can have very different CETs.

Can I pay off early? Yes — Law 10.931/2004 guarantees the right to settle anticipated installments with proportional interest discount. Always request the updated payoff balance from the lender.