Compound interest: the force that multiplies your money

Compound interest is interest calculated on the initial principal as well as on the accumulated interest from previous periods. The concept is simple, but its long-term effect is counterintuitive, which is precisely why it is worth understanding the math before relying on any simulation.

Simple vs. compound interest

With R$ 1,000 at 1% per month in simple interest, you earn R$ 10 every month. In 24 months, you will have R$ 1,240. With compound interest, the second month earns 1% on R$ 1,010, the third on R$ 1,020.10, and so on. In 24 months, the balance reaches approximately R$ 1,269.73. The difference may seem small over two years, but it widens rapidly over longer time horizons.

The formula is M = C × (1 + i)^n, where M is the final amount, C is the initial principal, i is the interest rate per period, and n is the number of periods. The rate and the time horizon must be in the same unit: a monthly rate with a term in months, an annual rate with a term in years.

Why time matters more than the rate

Imagine contributing R$ 500 per month at a hypothetical rate of 0.8% per month. In 10 years, the total contributed is R$ 60,000 and the balance reaches nearly R$ 100,000. In 20 years, the total amount contributed doubles to R$ 120,000, but the balance surpasses R$ 360,000. In other words, the second decade generates far more than the first because interest begins compounding on a much larger base.

The practical takeaway is that starting early with little often beats starting late with a lot. Someone who invests R$ 300 per month from age 25 to 35 and then stops can end up with an amount similar to someone who starts at 35 and contributes until age 60, depending on the rate. The simulation varies based on assumptions, but the underlying pattern remains the same.

The Rule of 72

To estimate how long it takes for an investment to double, divide 72 by the annual interest rate. At 6% per year, it takes about 12 years. At 9% per year, about 8 years. The rule works well for rates between 4% and 12% per year and helps you quickly tell whether a promised return is realistic: doubling your money in just a few months would require rates that no legitimate investment can guarantee.

The same mechanism in debt

Compound interest works against you when debts go unpaid. A revolving credit card balance carrying high monthly interest can double in just a few months. That is why paying off high-interest debt is usually the highest-yielding investment available to anyone who owes money.

What simulations don't show

Rates are not constant: the Selic (Brazil's benchmark interest rate) changes, equities fluctuate, and negative years happen. Income tax reduces net gains, and a fund's management fee also compounds—only in the asset manager's favor. An annual fee of 2% on total assets can consume a substantial portion of the final outcome over several decades.

Inflation is another critical factor. R$ 360,000 twenty years from now will not buy what R$ 360,000 buys today. For long-term goals, run simulations using a real rate—that is, discounting an estimate for inflation—or compare the projected result with the future cost of your goal.

How to put this into practice

Use the compound interest calculator on the website across three scenarios: conservative, moderate, and optimistic. Pay attention to how much of the final balance comes from contributions and how much comes from interest. Then, test the effect of increasing your contribution by R$ 100 versus starting two years earlier. In most scenarios, starting earlier delivers a greater impact than contributing more.