How long to triple at 8%?

Question

An investment earns 8\% per year with annual compounding. Solve in your head. Roughly how many years until it triples? Aim: under 15 seconds.

Accepted Answer

The rule of 72 gives the doubling time: 72 / 8 = 9 years per doubling. Now convert "triple" into doublings. Since 3 \approx 2^{1.58}, tripling takes about 1.58 doublings: 1.58 	imes 9 \approx 14.3 	ext{ years}. A handy shortcut for tripling directly is the rule of 114 (roughly 72 	imes \log2 3): 114 / 8 \approx 14.25 years, the same answer. Sanity check: the exact time is \dfrac{\ln 3}{\ln 1.08} = \dfrac{1.099}{0.077} \approx 14.3 years. Takeaway. The rule of 72 is really "years per doubling." For other multiples, count how many doublings the multiple is (3	imes \approx 1.58 doublings) or…

How long to triple at 8%?

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