Money quadruples in 12 years, what rate?

Question

An investment quadruples in 12 years with annual compounding. Solve in your head. Roughly what annual rate of return is that? Aim: under 10 seconds.

Accepted Answer

Quadrupling = doubling twice, so the money doubles every 12 / 2 = 6 years. Rule of 72 in reverse: 	ext{rate} \approx \frac{72}{6} = 12\%. Sanity check: exact rate is 4^{1/12} - 1 = 2^{1/6} - 1 \approx 12.2\%, the rule lands within a quarter point. Takeaway. Decompose growth multiples into doublings before reaching for the rule of 72: 4	imes is 2 doublings, 8	imes is 3, 10	imes \approx 3.3 doublings (because 2^{3.32} \approx 10). Then rate \approx 72 / (years per doubling), in either direction.

Money quadruples in 12 years, what rate?

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