Compound interest
Interest earned on interest - the mechanism that makes time worth more than amount.
Interest earned on interest - the mechanism that makes time worth more than amount.
Simple interest pays only on the principal; compound interest pays on the principal plus previously credited interest, so each period's return expands the base for the next. The force is exponential rather than linear - doubling a rate does not double the result, doubling the time does far more - which is why a small monthly contribution started early can outrun a much larger one started a decade later. Every APY quote on a savings or CD product is already a compounding figure.
Frequency is the detail people misread: at the same nominal rate, compounding monthly beats annual, and continuous compounding sits at the mathematical ceiling - which is why APY exists as the comparable all-in number. Debt compounds the same way in reverse, which is why minimum payments on revolving balances persist for years. The practical translation is identical in both directions: intervene early (save) or eliminate the base early (pay off), because the exponent does the rest.
Worked example
$10,000 at 5% simple interest earns $500 a year for thirty years - $15,000 total. Compounded annually at the same 5%, it becomes about $43,200 - $28,200 more from the same rate and the same start, earned entirely by interest on interest.
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