How long to double your money at 4%?

Question

An investment compounds at 4\% per year. Solve in your head. Roughly how many years until it doubles? Aim: under 5 seconds.

Accepted Answer

Rule of 72: doubling time \approx 72 / (	ext{rate in percent}). \frac{72}{4} = 18 	ext{ years.} Sanity check: the exact answer is \ln 2 / \ln 1.04 \approx 0.693 / 0.0392 \approx 17.7 years, so the rule overshoots by only about three months. At low rates the "true" numerator would be closer to \ln 2 	imes 100 \approx 69.3, giving 69.3/4 \approx 17.3 years, but 72 is used because it divides cleanly by so many common rates. For rates in the low single digits the rule is still very close. Takeaway. Divide 72 by the percentage rate for the doubling time. A 4\% rate needs about 18 years, and the…

How long to double your money at 4%?

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