In order to calculate the interest rate compounded continuously, we can use the formula:
[tex]A=P\cdot e^{rt}[/tex]Where A is the final amount after t years, P is the principal and r is the interest rate.
So, using A = 2P, P = 12500 and r = 0.09, we have:
[tex]\begin{gathered} 2P=P\cdot e^{0.09\cdot t} \\ 2=e^{0.09t} \\ \ln (2)=\ln (e^{0.09t}) \\ 0.693=0.09t\cdot\ln (e) \\ 0.693=0.09t \\ t=\frac{0.693}{0.09} \\ t=7.7 \end{gathered}[/tex]It will take 7.7 years to double the initial investment.
