Parcela Price (PMT)

Price system instalment

The Price (French amortisation) system keeps the instalment the same from the first payment to the last: PMT = PV · i / (1 − (1 + i)^(−n)), where PV is the financed amount, i the periodic interest rate and n the number of periods. Within each instalment the amortisation share keeps growing while the interest share keeps shrinking. Say PV = R$ 100,000, i = 1%/month, n = 100. That gives a PMT of about R$ 1,587 and a total of roughly R$ 158,700, of which R$ 58,700 is interest. Next to the SAC system, where amortisation is constant and the instalments fall over time, Price starts lighter but ends up costing more in interest. The name comes from British mathematician Richard Price, who worked out the table back in the 18th century.

Applications

You'll find it behind vehicle CDC (direct consumer credit), payroll loans (consignado), credit-card instalment plans, and real-estate financing in some bank programmes, though Caixa's SFH runs on SAC. It also shows up in BNDES Finame, leasing, mortgage calculators around the world, and any fixed-payment annuity, from bonds to pension annuities.

FAQ

Price or SAC, which is cheaper? SAC pays less interest overall, since it knocks down the principal faster. Price opens with smaller instalments but costs more by the end. Pick the one that fits your cash flow rather than asking which is objectively better.

Why does the instalment stay fixed if interest is compound? The formula picks the one PMT value that drains the balance to zero in n periods at rate i. Every instalment then splits into interest, charged on whatever balance is left, plus amortisation.

Does Brazilian CET include everything? Total Effective Cost (CET) wraps interest, fees, insurance and IOF into a single number. Compare loans by CET, never by the nominal rate.