Compound interest is interest calculated on the initial amount plus the interest already accumulated — the famous “interest on interest.” The formula is M = C × (1 + i)n. Over time, this effect makes your wealth grow along a curve rather than a straight line.
- With compound interest, the earnings from each period also earn returns in the following period.
- Basic formula: M = C × (1 + i)n, with rate and term in the same unit of time.
- R$ 10,000 at 10% a year for 10 years becomes R$ 20,000 with simple interest and R$ 25,937 with compound interest.
- Time, rate and regular contributions speed up the effect; costs, IR (income tax) and inflation slow it down.
- The same mechanism works against you in debts such as credit cards and overdraft (cheque especial).
What compound interest is
Interest is the price of money over time. When you lend your money — by buying a bond, a CDB (bank certificate of deposit) or leaving it in poupança (traditional savings account) — you receive interest as compensation. When you borrow money, you pay interest.
With compound interest, each period’s interest is added to the balance. In the next period, the rate applies to that larger balance. That is why people speak of “interest on interest”: today’s earnings become capital that earns tomorrow.
This is the regime used in the vast majority of investments and loans in Brazil. Tesouro Direto (Brazil’s retail government bond program), CDBs, LCIs and LCAs (tax-exempt real estate and agribusiness credit notes) and poupança all grow on a compound basis, as do credit card and overdraft debts.
At first, the difference compared with simple interest is small. Over the years, it becomes enormous. That is why time is considered an investor’s greatest ally.
The compound interest formula and how to calculate it
The compound interest formula for a one-time investment is:
M = C × (1 + i)n
Each term means:
- M (final amount): the ending value, including both principal and interest.
- C (capital): the initial amount invested (or borrowed).
- i (interest rate): the rate per period, in decimal form. 1% becomes 0.01; 10% becomes 0.10.
- n (number of periods): how many months or years the money stays invested.
If you only want to know how much it earned, just subtract the capital: J = M − C.
Worked example
Imagine you invest R$ 5,000 at a rate of 1% a month for 24 months, with no additional contributions.
- Identify the terms: C = 5,000; i = 0.01; n = 24.
- Add 1 to the rate: 1 + 0.01 = 1.01.
- Raise it to the number of periods: 1.0124 ≈ 1.2697.
- Multiply by the capital: 5,000 × 1.2697 ≈ R$ 6,348.67.
The accumulated interest was about R$ 1,348.67. With simple interest at the same rate, you would have R$ 6,200 (5,000 + 24 × R$ 50). The difference of almost R$ 150 comes solely from interest on interest — and it grows quickly over longer periods.
Converting an annual rate to monthly (and vice versa)
With compound interest, you cannot simply divide the annual rate by 12. The correct conversion is:
- Annual to monthly: imonthly = (1 + iannual)1/12 − 1
- Monthly to annual: iannual = (1 + imonthly)12 − 1
Example: with the CDI (Brazil’s interbank deposit rate) at about 13.65% a year in October 2026, the equivalent monthly rate is (1.1365)1/12 − 1 ≈ 1.07% a month. Going the other way, 1% a month is equivalent to about 12.68% a year — not 12%.
The rule of 72: a mental shortcut
The rule of 72 estimates how many years it takes for money to double: divide 72 by the annual rate (as a whole number, not a decimal).
- At 10% a year: 72 ÷ 10 = 7.2 years (the exact calculation gives about 7.3).
- At 13.65% a year: 72 ÷ 13.65 ≈ 5.3 years (the exact calculation gives about 5.4).
It is an approximation, useful for quickly comparing rates. It works best for rates between 6% and 12% a year and does not account for taxes or inflation.
Simple vs. compound interest: the difference in practice
With simple interest, the rate always applies to the initial capital. The earnings are the same every period, and growth is linear. With compound interest, the calculation base grows every period.
See what happens to R$ 10,000 invested at 10% a year, with no additional contributions:
| Year | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 1 | R$ 11,000 | R$ 11,000 | R$ 0 |
| 2 | R$ 12,000 | R$ 12,100 | R$ 100 |
| 3 | R$ 13,000 | R$ 13,310 | R$ 310 |
| 5 | R$ 15,000 | R$ 16,105 | R$ 1,105 |
| 10 | R$ 20,000 | R$ 25,937 | R$ 5,937 |
In the first year, the two regimes are tied. After ten years, compound interest generates almost R$ 6,000 more — and the gap keeps widening every year.
Simple interest shows up in specific situations, such as some calculations of fines and late-payment charges. For medium- and long-term investments, what matters is the compound logic.
Compound interest with monthly contributions
Few people invest a lump sum and forget about it. It is more common to invest a little every month. For that, you use the future value formula for a series of payments:
FV = PMT × [(1 + i)n − 1] ÷ i
- FV: accumulated future value.
- PMT: the monthly contribution amount.
- i: monthly rate (convert the annual rate using the formula in the previous section).
- n: number of months.
The formula assumes contributions at the end of each month. If you also have an initial amount, add the result of M = C × (1 + i)n to it.
The table below simulates monthly contributions at effective annual rates of 8% and 10% (equivalent to about 0.64% and 0.80% a month). These are hypothetical gross figures, before taxes, costs or inflation:
| Monthly contribution | Term | 8% a year | 10% a year | Total contributed |
|---|---|---|---|---|
| R$ 500 | 10 years | R$ 90,062 | R$ 99,932 | R$ 60,000 |
| R$ 500 | 20 years | R$ 284,500 | R$ 359,130 | R$ 120,000 |
| R$ 500 | 30 years | R$ 704,275 | R$ 1,031,422 | R$ 180,000 |
| R$ 1,000 | 10 years | R$ 180,124 | R$ 199,864 | R$ 120,000 |
| R$ 1,000 | 20 years | R$ 568,999 | R$ 718,259 | R$ 240,000 |
| R$ 1,000 | 30 years | R$ 1,408,551 | R$ 2,062,843 | R$ 360,000 |
Notice two things. First: over 10 years at 10% a year, interest accounts for about R$ 40,000 on top of R$ 60,000 contributed. Over 30 years, the balance tops R$ 1 million with R$ 180,000 contributed — interest becomes the largest part of the portfolio.
Second: doubling the term from 10 to 20 years more than triples the balance. Going from 20 to 30 years multiplies the balance by about 2.5 to 2.9 times, depending on the rate. That is the compound interest curve in action.
Compound interest calculator in Excel or Google Sheets
You don’t need to do the math by hand. A spreadsheet works as a compound interest calculator with the VF function (valor futuro, or future value — called FV in English versions):
=VF(taxa;nper;pgto;vp)
- taxa (rate): rate per period (monthly, if contributions are monthly).
- nper: number of periods.
- pgto (pmt): contribution for each period, with a negative sign.
- vp (pv): initial amount, also with a negative sign (use 0 if there is none).
The negative sign indicates money leaving your pocket; that way, the result shows up as positive. To reproduce the table above with R$ 500 a month, 10 years and 10% a year:
=VF((1+10%)^(1/12)-1;120;-500;0)
The result is about R$ 99,932. For the worked example (R$ 5,000 at 1% a month for 24 months, with no contributions), use =VF(1%;24;0;-5000), which returns approximately R$ 6,348.67.
The downside: compound interest on debt
The same force that multiplies investments multiplies debts. When you miss a bill payment or dip into your overdraft, the month’s interest is added to the outstanding balance, and the following month the rate applies to that larger amount.
The aggravating factor is the rate. Credit lines such as revolving credit card balances and overdrafts usually carry very high interest, far above any return you get from conservative investments. That is why debt grows faster than investments.
If you are already in debt, prioritize the debts with the highest interest, negotiate swapping them for cheaper credit lines and avoid paying only the minimum on your credit card bill.
What speeds up (and what slows down) compound interest
Looking at the formula, five factors determine the final result. Three work in your favor; two erode your returns.
Time
The term is in the formula’s exponent, which is why it carries the most weight. Starting early, even with a little, is usually worth more than starting late with a lot. In the contributions table, R$ 500 for 30 years beats R$ 1,000 for 20 years.
Rate
Small differences in rate become large differences in wealth. With R$ 1,000 a month for 30 years, going from 8% to 10% a year increases the balance by more than R$ 650,000. But be careful: a higher rate usually comes with higher risk.
Contributions
Regular contributions feed the base that earns returns. Increasing the amount you invest as your income grows speeds up the curve, and monthly discipline usually matters more than getting the timing right.
Costs and income tax
Management fees, custody fees and income tax reduce the effective rate. A hypothetical example: with R$ 1,000 a month for 30 years, dropping from 10% to 9% a year because of a 1-percentage-point cost reduces the final balance by about R$ 360,000.
In fixed income, IR follows a regressive table: 22.5% up to 180 days, 20% from 181 to 360 days, 17.5% from 361 to 720 days and 15% above 720 days. This favors those who leave their money invested longer. See the details in the guide to income tax on investments.
Inflation and real interest
Inflation is also compounded and erodes purchasing power. What matters is the real interest rate, calculated using the Fisher equation:
(1 + nominal rate) = (1 + real rate) × (1 + inflation)
Isolating the real rate: real rate = (1 + nominal) ÷ (1 + inflation) − 1. With the CDI at about 13.65% a year and the IPCA (Brazil’s official consumer price index) at 4.22% over 12 months (through August 2026), the gross real interest rate comes to around 1.1365 ÷ 1.0422 − 1 ≈ 9.05% a year, before IR. Simple subtraction (13.65 − 4.22) would give 9.43% — an approximation that overstates the gain.
How to put compound interest to work in practice
Understanding the formula is the first step. Putting compound interest to work takes a few simple habits:
- Pay off expensive debt first. There is no point investing at one rate while paying a much higher one.
- Build your emergency fund. It keeps you from redeeming long-term investments or turning to expensive credit when something unexpected happens. See how to build your emergency fund.
- Start now, even with a little. Time is the one factor you can’t get back later. The guide on how to start investing shows the first steps.
- Automate your contributions. Scheduling a transfer right after you get paid reduces the chance of spending before investing.
- Reinvest your earnings. Interest, dividends and distributions from FIIs (Brazilian real estate investment funds) that go back into the portfolio keep the snowball rolling.
- Compare costs and taxes. Choose products with low fees and consider the effect of IR over your chosen time frame. Tesouro Direto, for example, charges a custody fee of 0.20% a year, with an exemption on Tesouro Selic (the floating-rate government bond tied to the Selic rate) up to R$ 10,000.
- Look at the real interest rate. Assess whether your long-term investments are protected from inflation.
Conclusion
Compound interest is the foundation of virtually all investment math. The formula M = C × (1 + i)n shows that time, in the exponent, is the most powerful factor — and that small differences in rate and cost grow significantly over the years.
In October 2026, with the CDI at about 13.65% a year, even conservative investments clearly show this effect. But rates change, and the Focus survey (the Banco Central’s weekly market forecast report) projects a lower Selic (Brazil’s benchmark interest rate) in the coming years. That is why the most consistent strategy remains the same: start early, contribute regularly, reinvest, keep costs under control and steer clear of expensive debt. When you want to turn that wealth into cash flow, see the guide to passive income.
Frequently asked questions
What is compound interest, in a nutshell?
It is interest calculated on the initial capital plus the interest already accumulated. Each period, the previous earnings also start earning returns, which is why it’s called interest on interest.
What is the compound interest formula?
For a one-time investment, M = C × (1 + i)^n, where M is the final amount, C the capital, i the rate per period in decimal form and n the number of periods. With monthly contributions, use FV = PMT × [(1 + i)^n − 1] ÷ i.
What is the difference between simple and compound interest?
With simple interest, the rate always applies to the initial capital and growth is linear. With compound interest, it applies to the accumulated balance. R$ 10,000 at 10% a year for 10 years becomes R$ 20,000 with simple interest and R$ 25,937 with compound interest.
How do I convert an annual rate to a monthly rate?
Use the formula (1 + annual rate)^(1/12) − 1. For example, about 13.65% a year is equivalent to approximately 1.07% a month. Dividing the annual rate by 12 gives an incorrect result under compound interest.
How do I calculate compound interest in Excel?
Use the function =VF(taxa;nper;pgto;vp) (FV in English versions), with the contribution and initial amount as negative values. Example: =VF((1+10%)^(1/12)-1;120;-500;0) calculates R$ 500 a month for 10 years at 10% a year, resulting in about R$ 99,932.
What is the rule of 72?
It is a shortcut for estimating how many years it takes for money to double: divide 72 by the annual rate. At 13.65% a year, the result is about 5.3 years, close to the exact calculation of about 5.4 years.
This content is for educational purposes only and does not constitute an investment recommendation. Past performance does not guarantee future results. Data updated in October 2026.