Price Amortization Schedule

How the Price amortization table works

The Price system, also called French amortization after the 18th-century English actuary Richard Price, holds every installment at the same value: PMT = PV · i / (1 − (1 + i)^(−n)). Here PV is the present value, i the periodic rate and n the number of installments. Each row of the schedule still breaks into interest (balance × i) and principal (PMT − interest). As you go, the interest portion gets smaller and the principal portion grows, yet the payment you actually make stays flat.

Take R$ 100,000 financed at 1% per month over 100 months. The installment works out to about R$ 1,587, and across all of them you'd pay roughly R$ 158,700, of which something like R$ 58,700 is interest. That's more than SAC would charge at the same rate and term, and the reason is simple: the balance comes down slowly through the first half of the contract.

Real-world applications

In Brazilian consumer credit, Price is the system you'll find almost everywhere. Payroll-deductible loans (consignado), CDC vehicle financing, personal loans, refinancing and most credit-card installment plans (parcelado) are all built on a fixed installment. It also runs behind BNDES PEAC working-capital lines and most small-ticket auto loans. What makes it stick is predictability. Borrowers, and the credit-scoring models that size them up, would rather plan around a payment they already know.

FAQ

Why is the installment fixed if interest is decreasing? Each month, the principal portion goes up by exactly what the interest portion drops, so the two always add back to the same number. That trade-off is the entire point of the Price formula.

Why does Price end up paying more total interest than SAC? Early on, a Price installment barely touches the principal, so the balance sits high for longer and keeps piling up interest. SAC, by contrast, chips away at the principal much faster.

Is early payment worth it on a Price contract? Yes, and the first half is where it pays off most. BCB Resolution 4.292/2013 entitles you to a pro-rata interest discount when you settle early, and it's exactly in those early installments that the interest share is at its peak.