How to understand the interest on a debt

In a nutshell

Interest is the price you pay for using someone else's money, usually a bank's. On most debts, interest is compound: it is added to the debt and, the next month, it earns interest too. That is why a rate that looks small per month becomes a big number per year. Knowing this helps you choose the cheapest debt and pay off the most expensive one first.

Simple and compound interest

With simple interest, the rate always applies to the original amount. If you owe R$ 1,000 (Brazilian reais) at 8% a month, you pay R$ 80 in interest every month.

With compound interest, the rate applies to the amount that has already grown. It is "interest on interest". Credit cards, overdrafts and loans work this way.

Example

Carlos owed R$ 1,000 and paid nothing for 6 months. The rate is 8% a month. For reference, 8% a month is exactly the cap on overdraft interest for individuals and micro-entrepreneurs (MEI) in Brazil, in force since January 2020.

With compound interest, the debt grows like this:

• Month 1: R$ 1,000 × 1.08 = R$ 1,080.00
• Month 2: R$ 1,080.00 × 1.08 = R$ 1,166.40
• Month 3: about R$ 1,259.71
• Month 4: about R$ 1,360.49
• Month 5: about R$ 1,469.33
• Month 6: about R$ 1,586.87

With simple interest, it would be R$ 1,000 + 6 × R$ 80 = R$ 1,480.

The gap is about R$ 106.87 in just 6 months. The longer time runs, the wider it gets.

Monthly rate and yearly rate

Many offers in Brazil show the monthly rate because it looks smaller. To see the real weight, look at the yearly rate. It is not the monthly rate times 12, because interest builds on itself.

Suppose interest of 3% a month. Times 12 would give 36%. But with compound interest the math is 1.03 to the power of 12, which is about 1.4258. In other words, about 42.58% a year.

What CET means

The CET (Custo Efetivo Total, or total effective cost) adds up everything you pay on a loan: interest, fees, insurance and taxes. Two offers with the same interest rate can have a different CET. In Brazil, the bank must tell you the CET before you sign. Always compare by CET, not just by interest.

Step by step

1. Take the contract, statement or bill for each debt and write down the monthly interest rate.
2. Look for the yearly rate and the CET too. If they are not clear, ask the lender in writing.
3. Sort your debts from the highest rate to the lowest. Pay off or renegotiate the most expensive one first.
4. Compare your rates with market averages. Brazil's Central Bank publishes average rates by type of credit at Interest rates (in Portuguese).
5. To simulate how a debt will grow, use the Central Bank's Citizen's Calculator.
6. Before taking a new loan, ask for the CET of at least two offers and choose the lowest.

Common mistakes

• Looking only at the monthly rate. It looks small, but it adds up. Fix: always check the yearly rate.
• Multiplying the monthly rate by 12. That ignores interest on interest. Fix: use the yearly rate given by the lender or a calculator.
• Comparing offers by interest alone. Fees and insurance cost money too. Fix: compare by CET.
• Leaving the expensive debt for later. Every month it sits, it grows faster. Fix: tackle the highest-interest debt first.