Question 219496
{{{A = Pe^(rt)}}}
{{{P}}} is the original amount invested. The problem 
wants to know how long (what {{{t}}} is) it takes to
make {{{A}}} twice this amount, so {{{A = 2P}}}
{{{2P = Pe^(rt)}}}
given:
{{{r = .08}}} (this is annual intest rate)
{{{2P = Pe^(.08t)}}}
Divide both sides by {{{P}}}
{{{2 = e^(.08t)}}}
Take the natural log of both sides
{{{ln(2) = .08t}}}
{{{.69315 = .08t}}}
{{{t = 8.664}}} ({{{t}}} is the time in years)
I can find {{{.664}}} years in months also
{{{.664*12 = 7.9}}} (about 8 months)
It takes 8 years and 8 months to double money