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Compound Interest

fundamental concepts
Definition
Interest earned on both the initial principal and on previously accumulated interest — interest on interest.

Explanation

Compound interest is the single most powerful force in long-term investing. Albert Einstein allegedly called it the eighth wonder of the world. At 10% annual return: $10,000 becomes $25,937 in 10 years, $67,275 in 20 years, and $174,494 in 30 years. The Rule of 72 estimates doubling time: divide 72 by the return rate. At 10%, money doubles roughly every 7.2 years. Starting early matters enormously — an investor who starts at 25 will have roughly 4x more than one who starts at 35, assuming the same annual contributions and returns.

Formula

A = P(1 + r/n)^(nt)

Example

$10,000 invested at 8% annual return, compounded annually, for 30 years.

A = 10,000 × (1.08)^30 = 10,000 × 10.063 = $100,627

The original $10,000 grew to over $100,000 — more than $90,000 of that is compound interest, not the original investment.

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