Money grows eightfold in 18 years, what rate?

Question

An investment grows to eight times its value in 18 years with annual compounding. Solve in your head. Roughly what annual rate of return is that? Aim: under 15 seconds.

Accepted Answer

Eightfold = 2 	imes 2 	imes 2, three doublings. So the money doubles every 18 / 3 = 6 years. Rule of 72 in reverse: 	ext{rate} \approx \frac{72}{6} = 12\%. Sanity check: the exact rate is 8^{1/18} - 1 = 2^{1/6} - 1 \approx 12.25\%, so the rule lands within a quarter of a point. Takeaway. Decompose the growth multiple into doublings first: 8	imes is 3 doublings, so years-per-doubling = 18/3 = 6, and rate \approx 72 / 6. The rule of 72 runs in either direction once you know the doubling time.

Money grows eightfold in 18 years, what rate?

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