What return doubles your money in 8 years?

Question

The rule of 72 usually turns a rate into a doubling time. Here you are given the doubling time instead. Solve in your head.

What annual return do you need to double your money in $8$ years? Aim: under 5 seconds.

Accepted Answer

The rule is symmetric: rate 	imes years \approx 72. So 	ext{rate} \approx \frac{72}{8} = 9\%. Check: 1.09^{8} = 1.99, essentially a double. Takeaway. Because 72 \approx 	ext{rate} 	imes 	ext{doubling time}, you can solve for whichever quantity is missing. Given years, divide 72 by the years to get the rate; given the rate, divide 72 by the rate to get the years.

What return doubles your money in 8 years?

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