How long to quadruple your money at 8%?

Question

An investment compounds at 8\% per year. Solve in your head. Roughly how many years until it quadruples (grows fourfold)? Aim: under 10 seconds.

Accepted Answer

Quadrupling is two consecutive doublings, so just double the doubling time. One doubling at 8\% takes 72/8 = 9 years, so quadrupling takes 2 	imes 9 = 18 	ext{ years.} Equivalently, use the "rule of 144" for fourfold growth: 144 / 8 = 18 years, and 144 = 2 	imes 72 for exactly this reason. Sanity check: the exact answer is \ln 4 / \ln 1.08 \approx 1.386 / 0.0770 \approx 18.0 years, essentially spot on. The same chaining works for eightfold (three doublings, rule of 216) or sixteenfold (four doublings). Each additional doubling just adds one more 72/	ext{rate} block of years. Takeaway. Fou…

How long to quadruple your money at 8%?

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