The rule of 70 If you use the approximation ln 2 ≈ 0.70 (in place of 0.69314 . . .), you can derive a rule of thumb that says, “To estimate how many years it will take an amount of money to double when invested at r percent compounded continuously, divide r into 70.” For instance, an amount of money invested at 5% will double in about 70/5 = 14 years. If you want it to double in 10 years instead, you have to invest it at 70/ = 7% Show how the rule of 70 is derived. (A similar “rule of 72” uses 72 instead of 70, because 72 has more integer factors.)
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