The mathematics of compounding

Compounding is the process by which the returns on an investment themselves begin to earn returns. In the first period you earn on your principal; in every subsequent period you earn on the principal plus all accumulated gains. Because the base grows each period, the absolute gains accelerate — producing the characteristic exponential, rather than linear, growth curve.

Consider $10,000 invested at a 12% annual return. After one year the balance is $11,200. In the second year the 12% is applied to $11,200, not the original sum. After ten years the balance is approximately $31,000; after twenty, roughly $96,500 — with no additional contributions. The latter decade contributes far more in absolute terms than the first, precisely because the base is larger.

Two variables dominate the outcome: the rate of return and, more powerfully, time. Extending the horizon has a greater effect than marginally increasing contributions, which is why beginning earlier is so consequential. Conversely, every interruption — withdrawing capital, or sitting in cash — truncates the exponential and is disproportionately costly.

The Rule of 72 offers a quick approximation of doubling time: divide 72 by the annual percentage return. At 12%, capital doubles roughly every six years; at 8%, every nine. Use our compounding calculator to model your own assumptions.