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Mortgage instalment: how to calculate under SFH and SFI

A Brazilian mortgage (financiamento imobiliário) covers the property price after you subtract the down payment. With the Price system you get a flat instalment, PMT = PV · i / (1 − (1+i)⁻ⁿ). With SAC the principal you pay off each month stays fixed at A = PV / n, and the interest portion shrinks as the balance falls. Take a example: borrow R$ 400,000 for 360 months at 10% per year (roughly 0.7974% per month). Price gives you a steady PMT around R$ 3,510. SAC opens at about R$ 4,302 and drops to near R$ 1,120 by the end. You hand over less interest overall with SAC, but the early instalments hit harder.

Brazilian context: SFH, SFI, FGTS and 30% income cap

The SFH (Sistema Financeiro da Habitação, Law 4,380/1964) finances properties worth up to R$ 1.5M, holds rates to a regulated ceiling of TR + 12% per year, and lets the buyer tap FGTS (the employment severance fund) for the down payment, for amortization, or to pay the loan off. The SFI (Law 9,514/1997) drops the value cap but charges free-market rates. Since 2018 Caixa Econômica Federal, the biggest lender of the two, has run SAC by default; the private banks let you pick Price or SAC. Most lenders won't let the instalment pass 30% of household income. You see this used for a new build, a used property, a first home backed by FGTS, or financing straight from the developer.

FAQ

Does the instalment include insurance? Actual contracts tack on MIP/DFI insurance (covering life and property damage) plus an admin fee. The CET (Custo Efetivo Total) rolls all of that into one number, so compare the CET when you shop banks.

Should I shorten the term or lower the instalment when prepaying? Cutting the term saves you more in interest. Cutting the instalment frees up monthly cash. Either way, Brazilian law bans prepayment penalties on regulated mortgages.

What about TR? Most contracts are written as nominal + TR. The Taxa Referencial has sat near zero for years, though it can climb back into positive territory if Selic stays high.