How long does it to take to double your money at a given rate (r) ? Begin

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How long does it to take to double your money at a given rate \(r\) ? Begin with

\[F V=P V e^{r t}=2 P V\]

and approximate \(\ln (2) \approx 0.72\) to come up with the Rule of 72 .

(a) At \(3 \%\), approximately how many years does it take to double your money?

(b) How about at \(8 \%\) ?

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