Use formula to calculate continuously compounded interest
[tex]A=P\cdot e^{rt},[/tex]
where
P is the principal (initial) balance,
r is the rate of interest,
t is the time in years.
In your case, P=$5000, r=0.0675, A=$10000 (the amount of money should be doubled), then
[tex]\$10000=\$5000\cdot e^{0.0675t},\\ \\e^{0.0675t}=2,\\ \\0.0675t=\ln 2,\\ \\t=\dfrac{\ln 2}{0.0675}\approx 10.3.[/tex]
Therefore, you need about 10.3 years for the investment to double. If you consider the whole years, then you need 11 years.
Answer: 11 years
