The "Rule of 72" is used to easily estimate the time it takes for a magnitude to double at a given growth rate. It should be in the tool box of every "Do-It-Yourself" investor.
This is how it works. Suppose you get 8%/year on $2,000? How long will it take to grow to $4,000? The answer is 72/8 = 9 years.
You can check this by solving for x:
$4,000 = $2,000 * (1.08)^x
divide both sides by 2,000 and take logs of both sides:
log 2 = x log1.08 or x = log2/log1.08 = .301/.0334 = 9.01 years
Another problem:
Suppose the return is 9%/year. How many years to double? Answer: 8 years.
Suppose GDP grows at 4%/year. How many years will it take for the nation's output to double? Do this in your head. We know it takes 9 years at 8% so at 4% it will take twice as long, i.e. 18 years.
If you are interested in pursuing this further you may be interested in the following video. Professor Barlett uses 70 as the numerator which is a bit rougher of an approximation. The video is also worthwhile because it stresses "critical thinking", a topic du jour on college campuses.
I guess we'll never know the name of the medieval genius was who came up with the rule of 72.... probably an accountant/banker somewhere laboring over his ledger in candlelight. Compounding is the mathematical basis of investing, and investors should at least have a conceptual understanding of it.
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