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Compound interest is interest earning interest. Each period, the interest is added to the balance, and the next period's interest is calculated on that new, larger balance. This is the single most important idea in all of finance.

The formula

With PV as the starting amount, i the rate per period and n the number of periods:

FV = PV * (1 + i)^n

The exponent n is what makes growth accelerate — the balance grows geometrically, not in a straight line.

Worked example

The same R$ 1,000 at 1% per month, but now compounding, over 6 months:

FV = 1000 * (1 + 0.01)^6
FV = 1000 * 1.061520...
FV = 1,061.52

Compare with simple interest's R$ 1,060.00. The extra R$ 1.52 is interest earned on prior interest. Over 6 months it is tiny — but stretch it to 10 years (120 months):

FV = 1000 * (1.01)^120 = 1000 * 3.3004 = 3,300.39

The same deposit becomes R$ 3,300 compounding versus only R$ 2,200 with simple interest (1000 * (1 + 0.01 * 120)). Time is the multiplier.

Compounding frequency

The more often interest is added, the faster it grows. A nominal 12% per year gives different results depending on frequency:

Once a year: 1000 * (1.12) = 1,120
Monthly (1% * 12): 1000 * (1.01)^12 = 1,126.83

More frequent compounding always wins for the saver — and costs more for the borrower. We make this precise in the effective rate lesson.