Compound growth
The mechanism behind essentially every long-term financial outcome, good and bad. It is arithmetic, not magic, and the arithmetic is worth doing yourself once.
Compounding means earning a return on your returns. In year one you earn a return on what you invested. In year two you earn a return on the original amount plus the first year's gain. The base grows, so the same percentage produces a bigger number each time.
Year 1: $10,000 × 1.07 = $10,700
Year 5: $10,000 × 1.075 = $14,026
Year 10: $10,000 × 1.0710 = $19,672
Year 20: $10,000 × 1.0720 = $38,697
Year 30: $10,000 × 1.0730 = $76,123
Assumptions: a constant 7% annual return, no contributions, no fees, no tax. Real returns are never constant; this illustrates the mechanism, not an expectation.
Look at the shape of that. The first decade adds about $9,700. The third decade adds about $37,400 — nearly four times as much, from the same 7%. Nothing changed except the size of the base.
Why time beats rate
Most people optimise the return rate. The exponent matters more.
Saver A invests $10,000 at 7% for 30 years: $10,000 × 1.0730 = $76,123.
Saver B invests $10,000 at 9% for 20 years: $10,000 × 1.0920 = $56,044.
Saver A earned two percentage points less per year and finished with 36% more, purely from ten extra years.
The rule of 72
A shortcut worth memorising: divide 72 by the annual growth rate to approximate how many years it takes for money to double.
- At 3%: about 24 years.
- At 6%: about 12 years.
- At 9%: about 8 years.
- At 3.4% inflation: your purchasing power halves in about 21 years.
Compounding runs both ways
The same arithmetic applies to costs and to inflation, and it is just as powerful in the wrong direction.
At 7% gross: $10,000 × 1.0730 = $76,123
At 6% net of a 1% fee: $10,000 × 1.0630 = $57,435
Difference: $18,688 — roughly 25% of the final amount, from a fee that reads as a rounding error on a statement.
Compounding rewards two things you fully control — how early you start and what you pay in costs — far more than the one thing you do not control, which is the return itself.