Compound vs. Simple Interest.

Simple interest is calculated exclusively on the original principal balance, so the amount of interest earned or owed remains constant in each period. Compound interest, by contrast, is calculated on the principal plus any interest already accumulated, meaning interest earns interest over time and growth accelerates exponentially rather than linearly. The distinction is one of the most consequential in personal finance. On the investing side, compound interest — or more broadly, compound returns — is the force that turns modest, consistent savings into substantial wealth over long horizons. On the borrowing side, compound interest is the mechanism that makes high-rate debt so costly: credit cards that compound daily on an unpaid balance build debt far faster than the nominal annual rate might suggest. The mathematical difference between simple and compound growth becomes dramatic over long periods. At 8% simple interest on $10,000, an investor earns $800 every year for 30 years, accumulating $24,000 in interest. At 8% compounding annually, the same $10,000 grows to approximately $100,627 — more than four times as much — because each year's gains are folded into the new principal. Compounding frequency also matters: interest compounded monthly accumulates faster than interest compounded annually at the same stated rate, because the compounding intervals are shorter and interest begins earning interest sooner. Albert Einstein is apocryphally credited with calling compound interest the eighth wonder of the world, a quote that endures because the intuitive gap between simple and compound growth remains surprising even to financially literate people until they work through the arithmetic.