Compound Interest and Doubling Time Computed Mentally

The rule of 72, dividing 72 by the growth rate, estimates doubling time in seconds and stays accurate within days across common interview rates.

Computing doubling time mentally under compound growth relies on the rule of 72: divide 72 by the annual growth rate as a percentage, and the result is approximately the number of years needed for the amount to double. At an 8 percent annual rate, 72 divided by 8 is 9 years, and the true answer from the exact compounding formula is close enough, about 9.01 years, that the shortcut is accurate to a rounding error for any rate a trading interview would plausibly ask about.

The exact continuous-compounding doubling time is 100 times the natural log of 2 divided by the rate, which works out to roughly 69.3 divided by the rate rather than 72. Seventy two is used instead because it divides evenly by more small numbers, including 1, 2, 3, 4, 6, 8, 9 and 12, which matters more for mental arithmetic than the small accuracy loss it introduces at typical interest rates.

The approximation is most accurate for rates between about 6 and 10 percent, where the difference between 72 and 69.3 roughly cancels against the way discrete annual compounding runs slightly faster than continuous compounding. Outside that range, at very low or very high rates, the rule of 72 drifts from the true answer by more than a rounding error, and the rule of 70 is a marginally better approximation at low single-digit rates.

At 6 percent, 72 divided by 6 is 12 years to double. At 9 percent, 72 divided by 9 is exactly 8 years. At 12 percent, 72 divided by 12 is 6 years, and at 4 percent, 72 divided by 4 is 18 years. Each of these divisions is chosen to be clean specifically because 72 was picked for its factors, and a rate that does not divide evenly, such as 7 percent, gives an approximate 10.3 years rather than a whole number.

A position growing at 9 percent annually from 100,000 doubles to roughly 200,000 in 8 years under this approximation, and the exact compounding formula puts the true figure at 8.04 years, a difference of under three weeks on an 8-year horizon, the kind of quick sanity check candidates report using at systematic firms such as AQR Capital.