Definition
Called by Einstein 'the eighth wonder of the world' (attribution disputed but the principle is real). Compounding turns small consistent returns into large sums over decades. A $10,000 investment growing at 8% annually becomes ~$21,589 in 10 years, $46,610 in 20 years, and $100,627 in 30 years — the last decade adds nearly $54,000 by itself. The corollary: starting early matters far more than starting large. A 25-year-old investing $200/month can end up with more than a 35-year-old investing $400/month, both retiring at 65. Compounding also works against you with debt (credit cards, unpaid loans) — high interest compounds against the borrower.
A = P(1 + r/n)^(n·t)
A = final amount, P = principal, r = annual interest rate, n = compounding periods per year, t = years
Example
$10,000 principal at 8% annual return, compounded yearly over 30 years: A = 10,000 × (1.08)^30 = $100,627. Over 40 years: A = 10,000 × (1.08)^40 = $217,245 — more than doubling the 30-year result by adding just one more decade.
Frequently Asked Questions
What's the Rule of 72?
A quick mental shortcut: divide 72 by the annual return rate to estimate years to double your money. At 8% annual return, money doubles in ~72/8 = 9 years. At 12%: ~6 years. At 4%: ~18 years.
Does compounding work in a savings account?
Yes — high-yield savings accounts compound (typically daily or monthly). But real rates after inflation matter more than nominal rates: a 4% savings account with 3% inflation gives 1% real growth.
Can I lose money from compounding?
The math principle isn't the issue — negative annual returns compound losses too. A -20% year followed by a +20% year leaves you down 4% (100 → 80 → 96), not flat.