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Lesson 6 of 10

Compound Interest: The Formula, and Why It's Called the Eighth Wonder

EconomicsIntermediate

Interest on Interest

Simple interest pays you a fixed amount each period based only on your original principal. Compound interest pays you based on the ORIGINAL PRINCIPAL PLUS everything you've already earned - so each period's gain is a little bigger than the last, and the growth curve isn't a straight line, it bends upward.

text
A = P(1 + r)^t

A = final amount
P = principal (starting amount)
r = annual interest rate (as a decimal)
t = number of years
Line chart showing $10,000 growing at 7% annual compound interest over 30 years, reaching roughly $76,000.
$10,000 at 7% annually becomes roughly $76,000 after 30 years - more than seven times the original, entirely from the curve bending upward, not from adding new money.

The often-quoted attribution of "compound interest is the eighth wonder of the world" to Einstein is almost certainly apocryphal - there's no reliable source for him actually saying it. The math itself is real regardless of who first said the quote: the earlier money starts compounding, the more those extra years at the START of the curve matter, since that's the base every later year's growth builds on.

This is the entire mathematical argument for starting retirement savings early rather than "catching up later with bigger contributions" - a dollar invested at 25 has far more compounding years ahead of it than a dollar invested at 45, and no later lump sum fully makes up for lost time at the start of the curve.