Respuesta :
17 years (approximately)
1) Considering that we're going to need a formula for that Continuously Compounded, let's gather the data
F=double
rate: 4% (0.04)
Continuosly Compounded
Time: ?
2) Let's proceed writing it, and plugging it into the formula:
[tex]A=Pe^{rt}[/tex]Let's call the Future Value, A by "2P" since the Present Value is going to be doubled.
[tex]\begin{gathered} 2P=Pe^{rt} \\ 2P=Pe^{0.04t} \end{gathered}[/tex]2.2) Let's divide both sides by P, so we can get rid of "P" on the right side
[tex]\begin{gathered} 2P=Pe^{0.04t} \\ \frac{2P}{P}=\frac{Pe^{0.04t}}{P} \\ 2=e^{0.04t} \\ \end{gathered}[/tex]Let's apply logarithms on both sides:
[tex]\begin{gathered} \ln (2)=\ln (e)^{0.04t} \\ 0.04t=\ln (2) \\ t=\frac{\ln (2)}{0.04} \\ t=17.328\approx17 \end{gathered}[/tex]3) Hence, that investment will be doubled in approximately 17 years
