Loan Payment (PMT) Calculator
Calculate the fixed loan payment (PMT) using the amortization formula from the amount, interest rate and term. Plan loans and mortgage installments.
Monthly PMT
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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.
Related Tools
PMT Loan Payment Calculator
Compute fixed loan payment PMT = PV·i / (1−(1+i)^(−n)).
Loan Calculator
Simulate loans and financing with a full amortization table. Calculate installments, total interest, and the real cost of credit.
Personal Loan Interest
Compute installment and total interest of a personal loan via Price system, given principal, rate and term. Shows approximate CET.
Bond Dirty Price
Computes the dirty price of a bond: the clean price plus the interest accrued since the last coupon. The clean price is what shows up in quotes, but what actually changes hands at settlement is the dirty price, because the buyer has to reimburse the seller for the interest already run up. The tool works out the accrued interest on a linear basis and adds it to the clean price, returning both parts. Enter the clean price, the face value, the annual coupon rate, the coupon frequency, the days since the last coupon and the days in the period.
Outstanding Loan Balance at Month m (Fixed Payment)
Give the financed amount, monthly rate, term and month m for the balance PV(1+i)^m − PMT·((1+i)^m − 1)/i, Brazil's Price amortization.
Price Amortization Schedule
Generate Price amortization schedule (fixed payments) with interest/principal split.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.