The Mathematical Mechanics of Compounding
Compound interest is the mechanism whereby the returns on your capital earn returns of their own. Over short horizons, compounding produces modest results; over multi-decade intervals, it exhibits exponential growth curves that transform modest contributions into generational wealth.
The Rule of 72
To estimate how long it takes an investment to double at a constant annual return, divide 72 by the annual return rate. At an 8% expected nominal return, your portfolio doubles approximately every 9 years without additional contributions.
Time in the Market vs. Market Timing
The variable that exerts the greatest leverage in the compound interest formula is time ($t$). An investor who begins contributing $500 monthly at age 22 will amass significantly greater wealth by retirement than an investor contributing $1,000 monthly starting at age 35, despite injecting less total capital.