Compound interest: how it works in practice

Compound interest shows up in almost every financial decision: in the investment that earns every month, in the loan, in the overdue credit card. Understanding the mechanism helps you compare offers and notice when a number looks too good to be true.

All examples in this article are illustrative. The rates were chosen to make the math easy; they do not represent the return of any product and are not a promise of results. The calculations were checked by the editorial team.

Simple interest and compound interest

Interest is the price of money over time: lenders charge it, investors receive it.

• With simple interest, the rate always applies to the initial amount. R$ 1,000 at 1% a month earns R$ 10 a month, every month.
• With compound interest, the rate applies to the accumulated balance, which already includes previous interest. That is why it is called “interest on interest.”

Here are the first months with R$ 1,000 at 1% a month:

Month	Balance with simple interest	Balance with compound interest
0	R$ 1,000.00	R$ 1,000.00
1	R$ 1,010.00	R$ 1,010.00
2	R$ 1,020.00	R$ 1,020.10
3	R$ 1,030.00	R$ 1,030.30
6	R$ 1,060.00	R$ 1,061.52
12	R$ 1,120.00	R$ 1,126.83

At first, the difference is a matter of cents. In the second month, the extra R$ 0.10 is 1% interest on the R$ 10 from the first month.

The formula, demystified

The future value with compound interest is:

FV = PV × (1 + i)ⁿ

• PV is the present value (how much you invest or owe today);
• i is the rate per period, in decimal form (1% = 0.01);
• n is the number of periods, in the same unit as the rate.

In the example: 1,000 × 1.01¹² = 1,126.83. The rate and the term must be in the same unit. If the rate is monthly, the term is in months.

The Central Bank of Brazil’s Calculadora do cidadão (Citizen’s Calculator, in Portuguese) does this calculation under the “Valor futuro de um capital” (future value of capital) option: you enter the number of months, the monthly interest rate and the current capital.

Time is what makes the difference

The gap between simple and compound interest grows with the term. With the same R$ 1,000 at 1% a month:

Term	Simple interest	Compound interest
1 year (12 months)	R$ 1,120.00	R$ 1,126.83
5 years (60 months)	R$ 1,600.00	R$ 1,816.70
10 years (120 months)	R$ 2,200.00	R$ 3,300.39
20 years (240 months)	R$ 3,400.00	R$ 10,892.55

In 20 years, compound interest multiplies the amount by almost 11; simple interest, by 3.4. This is the effect often called the “snowball.” It works both ways: for those who invest and for those who owe.

A rule of thumb: the rule of 72

To estimate how long it takes for an amount to double, divide 72 by the rate per period. At 6% a year, 72 ÷ 6 = 12 years. The exact calculation gives 11.9 years. It is an approximation, useful for moderate rates; for high rates, the error increases.

Monthly and annual rates are not converted by multiplying by 12

This is one of the most common mistakes. A rate of 1% a month, compounded over 12 months, is equivalent to:

1.01¹² − 1 = 0.1268, that is, about 12.68% a year, not 12%.

The reverse also requires care. To find the monthly rate equivalent to an annual rate, use (1 + annual rate)^(1/12) − 1. When comparing two offers, put both rates in the same unit first.

In credit, the benchmark for comparison is the Custo Efetivo Total (CET), Brazil’s total effective cost of credit, which, under CMN Resolution No. 4,881/2020, must include interest, fees, taxes, insurance and other expenses of the transaction, not just the advertised interest rate.

Regular deposits

In practice, many people do not invest a single amount but deposit every month. In that case, each deposit earns for a different period: the first earns for the whole period, the last for just one month.

Illustrative example: R$ 200 deposited at the beginning of each month, for 120 months, at 0.8% a month.

• Total deposited: 200 × 120 = R$ 24,000.00.
• Final balance, with compound interest: about R$ 40,363.84.
• Portion that came from interest: about R$ 16,363.84.

The calculation uses the formula for deposits at the beginning of the period: 200 × [(1.008¹²⁰ − 1) ÷ 0.008] × 1.008. If the deposits were made at the end of each month, the result would be R$ 40,043.49. The Citizen’s Calculator has an “Aplicação com depósitos regulares” (investment with regular deposits) option, which assumes the deposit is made at the beginning of the month.

In real life, the result will be different. Investment rates vary, there are taxes, management fees and, in many products, the risk of loss. No investment guarantees a constant rate for ten years just because the math was done that way.

The debt side

The same mechanism that makes an investment grow makes a debt grow, and usually faster, because credit rates tend to be higher than investment rates.

Illustrative example, unrelated to any institution’s rate: a debt of R$ 1,000 at 10% a month, with no payments.

• After 7 months: R$ 1,948.72.
• After 8 months: R$ 2,143.59 (more than doubled).
• After 12 months: R$ 3,138.43.

In Brazil, revolving credit and credit card bill installment plans have a legal cap. Law No. 14,690/2023 established that, in the absence of limits approved through self-regulation, the total interest and financial charges cannot exceed the original amount of the debt (Law No. 14,690/2023, Art. 28). CMN Resolution No. 5,112/2023 regulated the rule, defined what counts as the “original amount of the debt” and requires bills and statements to show how much has already been charged and how much can still be charged.

In the example above, this means that interest and charges combined could not exceed R$ 1,000. Even so, the debt would double. And the cap applies to these credit card products, not to every type of credit.

Nominal interest, inflation and real return

A 10% annual return does not mean you became 10% richer. Part of it only offsets inflation. The real return is calculated as follows:

(1 + nominal rate) ÷ (1 + inflation) − 1

Illustrative example: a 10% return and 4% inflation over the same period. 1.10 ÷ 1.04 − 1 = 0.0577, or about 5.77% in real terms, not 6%.

For a concrete reference, the 12-month IPCA (Brazil’s official consumer inflation index) through August 2026 was 4.22%, according to IBGE (SIDRA, table 1737). This figure says nothing about future inflation. The article on inflation: causes, measurement and consequences explains how the index is measured.

Before comparing, also deduct the product’s taxes and fees. It is the net, real return that shows how much your purchasing power changed.

What to watch for in a simulation

• Check the rate’s unit. Monthly or annual? Nominal or effective?
• Be wary of fixed rates over long periods. Simulations assume a constant rate that rarely holds.
• Ask about risk. Higher returns usually come with higher risk, including partial or total loss.
• Consider costs and taxes. They also accumulate over time.
• A promise of high, guaranteed returns is a red flag. See the article on digital financial scams.

Key takeaways

• Compound interest applies to the accumulated balance; the formula is FV = PV × (1 + i)ⁿ, with rate and term in the same unit.
• The effect grows over time: R$ 1,000 at 1% a month becomes R$ 1,126.83 in one year and R$ 3,300.39 in ten years.
• 1% a month is not 12% a year, but about 12.68%.
• The mechanism also makes debts grow fast; on revolving credit card debt there is a legal cap on interest and charges.
• What matters is the real return, net of inflation, costs and taxes, and no numerical example guarantees future results.