What compound interest is
With compound interest, the return of each period is added to the capital and starts earning interest in the next period too. This is the famous “interest on interest”, and it is why money grows at an accelerating pace over time.
M = C × (1 + i)n, where M is the final amount, C the initial capital, i the rate per period and n the number of periods.
With monthly deposits
The calculator adds a deposit at the end of each month: balance = balance × (1 + i) + deposit. That way you can see the difference between the total that came out of your pocket and the total that interest produced.
Example: R$ 1.000 to start, R$ 500 per month, a rate of 10% per year for 10 years. You invest R$ 61.000 and the final amount is about R$ 102.500, which means more than R$ 41.000 comes from interest alone.
Monthly or annual rate
Annual and monthly rates are not converted by dividing by 12. The monthly rate equivalent to 12% per year is (1,12)1/12 − 1 ≈ 0,949% per month, not 1%. The tool makes this conversion and shows the equivalent rate.
Simple interest vs. compound interest
With simple interest, the return always applies to the initial capital (it grows along a straight line). With compound interest it applies to the current balance (it grows along a curve). The longer the term, the bigger the difference.
Example: R$ 500 per month at 10% per year
Monthly deposits of R$ 500, no initial amount, earning 10% per year (deposit at the end of each month):
| Term | Total invested | Final amount | Interest |
|---|---|---|---|
| 10 years | R$ 60.000,00 | R$ 99.931,93 | R$ 39.931,93 |
| 20 years | R$ 120.000,00 | R$ 359.129,61 | R$ 239.129,61 |
| 30 years | R$ 180.000,00 | R$ 1.031.421,66 | R$ 851.421,66 |
After 30 years, 83% of the final amount comes from interest. It is time, not the size of the deposit, that makes the curve climb.
Monthly vs. annual rate: conversion table
| Monthly rate | Equivalent annual rate |
|---|---|
| 0,5% per month | 6,17% per year |
| 0,797% per month | about 10% per year |
| 1% per month | 12,68% per year |
| 1,5% per month | 19,56% per year |
For the reverse path, 12% per year is equivalent to about 0,949% per month, not 1%. To check a quick calculation, use the online calculator.
Rule of 72
To estimate how long it takes for an amount to double, divide 72 by the annual rate in percent. At 10% per year, 72 ÷ 10 = 7,2 years (the exact calculation gives 7,27). At 6% per year, about 12 years. It is a useful approximation for rates between 4% and 15%.
Real return: discounting inflation
The gain in purchasing power is the real return: (1 + nominal rate) ÷ (1 + inflation) − 1. An investment at 10% per year with inflation of 4,5% earns 1,10 ÷ 1,045 − 1 ≈ 5,26% per year in real terms. The calculator shows the nominal amount; adjust the rate for inflation to see the real value.
Income tax (Imposto de Renda) and returns
The calculator’s result is gross. For fixed-income investments in Brazil, such as CDB (bank certificates of deposit) and Tesouro Direto (government bonds), the income tax (IR) is regressive: 22,5% up to 180 days, 20% from 181 to 360 days, 17,5% from 361 to 720 days and 15% beyond 720 days. Poupança (the savings account) and LCI/LCA (real-estate and agribusiness credit notes) are exempt for individuals. Also consider management and custody fees.
When compound interest works against you
The same effect applies to debt: credit cards and overdrafts charge interest on interest. In a loan, the rate and the term define how much extra you pay; compare the systems in the SAC and Price financing simulator. And if you want to invest your 13th-month salary, first work out the amount in the 13th-month salary calculator.
Compound interest by deposit and term
See what each combination of monthly deposit and term earns in the table by deposit and term, or pick a scenario:
- R$ 100 per month for 10 years
- R$ 100 per month for 20 years
- R$ 100 per month for 30 years
- R$ 300 per month for 10 years
- R$ 300 per month for 20 years
- R$ 300 per month for 30 years
- R$ 500 per month for 10 years
- R$ 500 per month for 20 years
- R$ 500 per month for 30 years
- R$ 1.000 per month for 10 years
- R$ 1.000 per month for 20 years
- R$ 1.000 per month for 30 years
Compound interest by amount invested
Want to know what a lump sum earns, with no monthly deposits? See the table by amount invested and term, or pick a scenario:
- R$ 5 thousand invested for 5 years
- R$ 5 thousand invested for 10 years
- R$ 5 thousand invested for 20 years
- R$ 10 thousand invested for 5 years
- R$ 10 thousand invested for 10 years
- R$ 10 thousand invested for 20 years
- R$ 20 thousand invested for 5 years
- R$ 20 thousand invested for 10 years
- R$ 20 thousand invested for 20 years
- R$ 50 thousand invested for 5 years
- R$ 50 thousand invested for 10 years
- R$ 50 thousand invested for 20 years
Frequently asked questions
What is the compound interest formula?
M = C × (1 + i)^n. With periodic deposits, the same calculation is applied month by month: balance = balance × (1 + i) + deposit.
How do I convert an annual rate into a monthly rate?
Raise (1 + annual rate) to the power of 1/12 and subtract 1. For example, 12% per year is equivalent to about 0,949% per month.
Does the calculator deduct income tax?
No. The result is gross. Fixed-income investments have regressive income tax and other fees that depend on the product and the term.
Are deposits made at the start or the end of the month?
At the end of each month. This is slightly more conservative than depositing at the start.
Are the results guaranteed?
No. It is a simulation with a constant rate. Actual returns vary and past returns do not guarantee future results.
How much does R$ 500 per month earn in 10 years?
At 10% per year, with deposits at the end of each month, R$ 500 per month grows to about R$ 99.932 in 10 years, of which R$ 60.000 is the total invested. The result varies with the actual rate you get.
What is the rule of 72?
It is an estimate of the time it takes for an amount to double: divide 72 by the annual rate in percent. At 10% per year, the amount doubles in about 7,2 years.
Sources and references
Informational content only, not legal, accounting or financial advice. Always check the official sources.