Question 851560
Are you given {{{ A }}}, {{{ P }}} and {{{ i }}} ?
Say they are given. 
{{{ A = 2000 }}}
{{{ P = 500 }}}
{{{ i = .06 }}}
You are asked to find {{{ N }}}
{{{ A = P*( 1 + i )^N }}}
{{{ 2000 = 500*( 1 + .06 )^N }}}
Divide both sides by {{{ 500 }}}
{{{ 4 = 1.06^N }}}
Now you take the log of both sides
{{{ log(4) = log(( 1.06^N )) }}}
{{{ log(4) = N*log(( 1.06 )) }}}
{{{ N = 1og(4) / log(( 1.06 )) }}}
{{{ N = .6021 / .0253 }}}
{{{ N = 23.8 }}}
So, it takes 24 yrs ( rounded off ) for $500
invested @ 6%, compounded annually to
become $2,000
check:
{{{ 2000 = 500*( 1 + .06 )^N }}}
{{{ 2000 = 500*( 1 + .06 )^24 }}}
{{{ 4 = 1.06^23.8 }}}
By my calculator:
{{{ 4 = 4.002 }}}
close enough