The rule and why it works
Money at r% a year doubles in roughly 72 ÷ r years: 6% doubles in 12, 8% in 9, 3% in 24. The exact doubling time is ln 2 ÷ ln(1+r), and 72 is the divisible-by-everything integer that tracks it closely across ordinary rates — within a few percent from 4% to 12%, slightly generous below that, slightly stingy above. (Purists use 69.3 for continuous compounding; nobody at dinner is compounding continuously.)
Three daily uses
Pricing a horizon. At the house's 6% default, a ten-year purchase decision faces most of one doubling: the sticker times ~1.8 is the wealth actually on the table. This is the opportunity-cost principle at mental-math speed, and it is why True Cost results stop feeling surprising once the rule is internalised.
Pricing an enemy. Run it on inflation: at 3.5%, prices double — money halves — in about 20 years; at 7%, in 10. A "safe" account at 1% under 3.5% inflation is a slow halving with a statement attached, which is Idle Cash in one line.
Pricing fees and drags. The rule works on differences too: a 2-point fee on a 7% return doesn't cost "2%", it moves the doubling from ~10 years to ~14 — over a working life, roughly one entire doubling of terminal wealth. Small rates, long horizons, brutal totals.
The caution
Whoever quotes compounding at you is choosing the rate and the horizon. The rule cuts both ways: it exposes the optimistic 12%-forever pitch (money 8×'s in 18 years — really?) just as fast as it prices your idle cash. Keep the integer; audit the inputs.