Brazilian loan calculator: SAC vs Price, table and CET

1. Amount financed and monthly rate

The amount financed is price − down payment. Interest is charged monthly, so the simulator always works with a monthly rate. If you enter an annual rate, it is converted using compound-interest equivalence: monthly rate = (1 + annual rate)^(1/12) − 1. Dividing by 12 is not enough: 12% a year is about 0.95% a month, and 1% a month is about 12.68% a year. Both rates appear in the result.

2. SAC (constant amortisation)

Under SAC (Sistema de Amortização Constante), the principal is repaid in equal parts: principal = amount financed ÷ term. Each month, interest is balance × monthly rate and the instalment is principal + interest. Because the balance falls at a steady pace, interest shrinks, so instalments start higher and end lower.

3. Price (constant instalment)

The Price table is the standard annuity: instalment = PV × i ÷ (1 − (1 + i)^−n), where PV is the amount financed, i the monthly rate and n the term in months. Early instalments are mostly interest, and the principal share grows over time. Since the balance falls more slowly at first, total interest under Price is higher than under SAC for the same rate and term. At zero interest both systems give equal instalments.

4. Insurance, fees and approximate CET

You can enter monthly insurance and fees (added to every instalment) and upfront fees paid in cash when signing. The simulator then calculates an approximate CET (Custo Efetivo Total, the all-in annual cost banks in Brazil must disclose): the internal rate of return of a cash flow in which you receive amount financed − upfront fees and pay instalment + monthly insurance and fees each month. The monthly rate found is annualised with (1 + rate)^12 − 1. With no insurance or fees, the CET equals the equivalent annual interest rate.

The real CET quoted by a bank also includes IOF (a federal tax on credit operations) and bank-specific items such as appraisal and registration fees. That is why the figures on your bank's CET statement prevail over this estimate. Banco Central (Brazil's central bank) requires lenders to disclose the CET before signing; ask for it and compare.

What the simulator leaves out

• Inflation or index adjustment of the balance (TR, IPCA or others), common in Brazilian mortgages.
• Insurance that varies with the balance or the borrower's age; here the monthly amount is fixed.
• IOF, grace periods, extra repayments and use of FGTS savings.

Results are estimates for comparing scenarios; the bank's formal offer is the official reference. To share the scenario, use Copy simulation link.

In the example, an asset priced at R$100,000.00 is bought with R$20,000.00 down, so the amount financed is R$80,000.00, at 1% a month (about 12.68% a year) over 12 months, with no insurance or fees. Under SAC the principal is R$6,666.67 a month; the first instalment is R$7,466.67 and the last R$6,733.33, with R$5,200.00 of interest and R$85,200.00 paid in total. Under Price the fixed instalment is R$7,107.90, with R$5,294.84 of interest and R$85,294.84 in total. SAC pays R$94.84 less interest in exchange for higher early instalments. With no extra costs, both approximate CETs equal the equivalent annual rate, 12.68%.