Rule of 72

A reliable mental shortcut for doubling time is the “Rule of 72”: divide 72 by the annual rate of return, in percent, and you have the number of years.

As you can see in Table 2.1, this approximation is pretty good for practical purposes, with error increasing towards high rates and rates close to zero. The 72 is not arbitrary: doubling at rate $r$ takes $\text{ln}<!--\; FUNCTION\; APPLICATION\; -->2∕\text{ln}<!--\; FUNCTION\; APPLICATION\; -->(1+r)\approx 69.3∕r$ years (in percent terms), and 69.3 is nudged up to 72 because it fits typical 6–10% rates better and divides evenly by 2, 3, 4, 6, 8, 9, and 12. That origin is also why the table’s error grows at the extremes — the nudge is calibrated to the middle.

The rule’s real job is converting small rate differences into years, which is where it earns a permanent place in your head. At 7% money doubles about every 10 years; give up one point to fees and, at 6%, each doubling takes 12. Over a 36-year career that is 3.6 doublings shrunk to 3 — roughly a third of your terminal wealth surrendered to a difference that was described to you as “only one percent.” Run the rule whenever someone tells you a fee is small.