Compound Interest Calculator

How does compound interest work?

With compound interest, the interest earned in each period becomes part of the principal and keeps earning in the periods that follow. In the basic formula A = P × (1 + r)ⁿ, A stands for the amount, P the principal, r the rate and n the period.

Once recurring monthly contributions come in, the math treats each deposit as earning interest for however many periods are left. That is where the well-known "snowball effect" comes from.

How compound interest actually works

The compound interest formula is M = C · (1 + i)^t. Here M is the final amount, C is the initial capital, i is the interest rate per period written as a decimal (1% means 0.01), and t is the number of periods. Everything turns on that exponent. Each period earns interest on the previous balance, and that balance already includes interest earned before. Simple interest, by contrast, is linear (M = C · (1 + i · t)) and ignores the recursion completely.

Take the Selic rate, Brazil's benchmark short-term interest rate. In early 2026 the Copom held Selic near 15% per year. Put R$ 10,000 to work at 15% per year for 10 years and compound interest turns it into R$ 40,455.58, while simple interest stops at R$ 25,000. That R$ 15,455 gap is nothing but the snowball effect. People like to quote Einstein calling compounding "the eighth wonder of the world", and the line is almost certainly apocryphal (no contemporary source ties it to him), but the math earns the reverence anyway.

Monthly contributions and the future value formula

Add a fixed monthly contribution PMT and the future value becomes FV = C · (1 + i)^t + PMT · ((1 + i)^t − 1) / i. That is the equation most investment calculators run under the hood. One catch: i and t have to share the same time unit. If your rate is annual but you contribute monthly, convert it with the equivalent rate i_month = (1 + i_year)^(1/12) − 1 rather than dividing by 12, which would give you a nominal rate instead of the effective one.

Brazilian fixed-income products quote rates in their own way. A CDB at "110% of CDI", with CDI tracking Selic at 15% per year, yields roughly 16.5% gross per year, but income tax takes a bite between 22.5% (under 180 days) and 15% (over 720 days). Tesouro Selic and most CDBs follow this regressive table, while LCI and LCA are exempt. For a realistic projection, plug the net rate into the calculator above.

FAQ

Why does a small rate difference matter so much over time? Because the exponent compounds the difference too. R$ 1,000 at 8% per year for 30 years becomes R$ 10,062. At 10% it becomes R$ 17,449. So a rate that is 25% higher ends up producing 73% more money.

What is the Rule of 72? It's a back-of-envelope shortcut. Divide 72 by the annual interest rate and you get the approximate number of years it takes to double your money. At 8% per year, that's roughly 9 years; at 12%, about 6. For rates between 5% and 15% the approximation stays within 1%.

Does this calculator account for inflation? No, the result is nominal. For the real, inflation-adjusted return, subtract the inflation rate from the interest rate before you plug it in. With IPCA running around 4% per year against a 15% nominal yield, the real return comes to roughly 10.6% via the Fisher equation: (1.15 / 1.04) − 1.

Compound interest works against me on debt too? Yes, and far more aggressively. Brazilian revolving credit card debt averages above 400% per year, so an untouched R$ 1,000 balance balloons to R$ 5,000 within a single year. It is exactly the same formula, just sitting on the other side of the table.