PRICE or SAC: how each system works and which to choose

When you finance a car or a home, or take out a personal loan, every installment pays for two things at once: the interest for the period and a slice of the debt, called amortization. What changes from one amortization system to another is how that split plays out over time. In Brazil, the two most common are the PRICE table and the SAC.

What amortizing means

To amortize is to reduce the outstanding balance. Each month's interest is charged on the balance that is still open: interest = outstanding balance × monthly rate. What is left of the installment after paying the interest pays down the debt. The faster the balance falls, the less interest you pay in the following months, and that speed is what sets the two systems apart.

How the PRICE table works

In PRICE, also known as the French system, every installment has the same value. Because the balance is high at the start, most of the first installments is interest and only a small part pays down the debt. As the months go by, interest shrinks and amortization grows, until the last installment.

The fixed installment comes from this formula: PMT = PV × i × (1 + i)^n / ((1 + i)^n − 1), where PV is the amount financed, i is the rate per period and n is the number of installments.

How the SAC works

In the SAC (Constant Amortization System), the amortization is the same every month: the amount financed divided by the number of installments. Interest is charged on a balance that falls steadily, so the installment starts higher and gets smaller each month.

An example with numbers

Consider a loan of R$ 10,000.00 in 6 installments, at 12% a year (a nominal rate, equivalent to 1% a month). Here is what each system charges month by month:

The PRICE installment stays at R$ 1,725.48 (the last one absorbs the rounding cents). The SAC one starts at R$ 1,766.67 and ends at R$ 1,683.32. In the end, SAC cost R$ 2.91 less in interest. Over 6 months the difference is small, but it grows with the term and with the amount financed:

Which one to choose

There is no system that is best for everyone. What exists is a trade-off:

• SAC usually costs less in total, because it amortizes faster. It needs a higher first installment and relies on an income that can carry it at the start of the contract.
• PRICE has a fixed installment that is lower at the start, which makes it easier to fit the debt into the budget and to plan the coming months. In exchange, it pays more interest in total.
• On home loans, banks limit how much of your income the installment can take. Since the first SAC installment is higher, it may reduce the amount the institution approves.

Two questions help: which installment fits your budget today? And is your income likely to rise, stay steady or fall over the contract? Someone who expects a higher income later can absorb the higher first SAC installment. Someone who needs complete predictability may prefer PRICE.

What matters besides the system

Choosing between PRICE and SAC is only one decision. Before you sign, also compare:

• The interest rate. A lower rate on PRICE can cost less than a higher rate on SAC. Check whether the rate is monthly or yearly and whether it is nominal or effective: see the guide on nominal and effective rates.
• The charges. Fees, insurance and IOF tax are part of the cost of the operation, and the CET puts it all into one rate.
• The term. A longer term lowers the installment and raises total interest in both systems.
• Early repayment. Paying part of the debt before the term cuts future interest. It is worth comparing with investing that money.

How to simulate with your own numbers

In the simulator, enter the amount, the rate and the term and pick PRICE or SAC in "Amortization type": the schedule shows, month by month, how much of each installment is interest and how much pays down the debt. To put proposals from different institutions side by side, use the comparison screen.