Answer: 6.93 years
Step-by-step explanation:
Given
Rate of interest is [tex]r=10\%[/tex]
Future value is given by [tex]s=1000e^{0.1t}[/tex]
For the investment to double itself, i.e. [tex]s=2000[/tex]
[tex]\Rightarrow 2000=1000e^{0.1t}\\\Rightarrow 2=e^{0.1t}\\\\\text{Taking log both sides}\\\\\Rightarrow \ln 2=0.1t\\\\\Rightarrow t=\dfrac{\ln 2}{0.1}\\\\\Rightarrow t=6.93\ \text{years}[/tex]
It takes around 6.93 years to double the investment.
