How Compounding Works
Compounding is what happens when a return is left to earn on itself. The shape it creates over long periods is the single most important pattern in finance.
Simple interest vs compound interest
Simple interest pays a fixed amount each year based only on the original principal. Compound interest pays interest on the running balance — including past interest.
Simple: FV = P × (1 + r × n) Compound: FV = P × (1 + r) ^ n
At low rates over short periods the two are close. At higher rates or longer periods the gap grows fast.
Why compounding is non-linear
Each year, the return is applied to a bigger base. After 30 years at 10%, most of the gain in the final year is interest on prior interest, not interest on the original principal.
The S-curve of long-horizon compounding
The first decade of a long-horizon investment usually feels slow. Then it accelerates. Then it gets dramatic. People who stop early never see the part where the curve bends sharply upward.
Compounding frequency
Compounding can happen annually, quarterly, monthly, daily, or continuously. Higher frequency means slightly more for the same nominal rate, but the effect is much smaller than people assume:
8% annual: 1.0800 after 1 yr 8% monthly: 1.0830 after 1 yr 8% daily: 1.0833 after 1 yr 8% continuous:1.0833 after 1 yr