Question 541357
{{{A=Principal*e^(rate*time)}}}
Take natural logarithms on both sides
{{{ln(A)=ln(Principal)+rate*time}}} subtract from both sides {{{ln(Principal)}}}
{{{ln(A)-ln(Principal)=rate*time}}} use properties of natural logaritms
{{{ln(A/Principal)=rate*time}}}
Now we how we can substitute that doubled the investment bit.
{{{ln(2)=rate*9}}}
Your calculator or spreadsheet software can calculate {{{ln(2)}}}
I calculated {{{rate=ln(2)/9= 0.077016}}}, meaning annual rate=7.7016%
Rounding  to 7.7% (or to 7.70%) you end up a few cents short at 9 years, but maybe it's close enough.