How long to triple your money at 6%?

Question

Everyone knows the rule of 72 for doubling. There is a matching rule for tripling: divide $114$ by the growth rate. An investment compounds at $6\%$ a year. Solve in your head.

Roughly how many years until it triples? Aim: under 10 seconds.

Accepted Answer

Use the rule of 114: \frac{114}{6} = 19 	ext{ years.} Check against the truth: tripling needs \ln 3 / \ln 1.06 = 1.099 / 0.0583 \approx 18.9 years. The rule nails it. Takeaway. The constant is 114 because 100 	imes \ln 3 \approx 109.9, bumped up to 114 so the estimate stays accurate across ordinary rates (just as 72 beats the "true" 69.3 for doubling). Companion rule: use \approx 165 for a five-fold increase.

How long to triple your money at 6%?

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