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# what rate of interest compounded continuously is required to double an investment in 3 years?

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what rate of interest compounded continuously is required to double an investment in 3 years?

May 9, 2022

#1
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Ln(2) / 3 ==23.105% compounded continuously will double your money in 3 years.

May 9, 2022
#2
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Let r% be such rate of interest.

$$P\displaystyle\lim_{n\to\infty}\left(1 + \dfrac{r\%}n\right)^{3n} = 2P\\ e^{3r\%} = 2\\ 3r\% = \ln(2)\\ r\% = \dfrac{\ln(2)}3 \approx 0.231$$

The rate must be at least 23.1%.

May 9, 2022