Question 580458
This is the right place ( unless I'm in the wrong place )
I will say: {{{ x = 50000 }}}
After 1 yr she will have:
{{{ x - .05x }}}
After 2 yrs she will have
{{{ x - .05x - ( .05*( x - .05x ) ) }}}
After 3 yrs she will have:
{{{ x - .05x - ( .05*( x - .05x ) ) - ( .05*( x - .05x - ( .05*( x - .05x ) ) ) ) }}}
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A little too complicated. Go back to the 2nd step
and factor out {{{ x - .05x }}}
{{{ x - .05x - ( .05*( x - .05x ) ) = ( x - .05x ) * ( 1 - .05 ) }}}
and {{{  ( x - .05x ) * ( 1 - .05 ) = x*( 1 - .05 )*( 1 - .05 ) }}}
and {{{ x*( 1 - .05 )*( 1 - .05 ) = x*( 1 - .05 )^2 }}}
A lot better
Now plug this into step 3 where you see {{{ x - .05x - ( .05*( x - .05x ) ) }}}
{{{ x - .05x - ( .05*( x - .05x ) ) - ( .05*( x - .05x - ( .05*( x - .05x ) ) ) ) }}}
{{{  x*( 1 - .05 )^2 - .05*(  x*( 1 - .05 )^2 ) }}}
This time factor out {{{  x*( 1 - .05 )^2 }}}
{{{ x*( 1 - .05 )^2 * ( 1 - .05 ) }}}
{{{ x*( 1 - .05 )^3 }}}
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This is the rule. If you start with {{{ x }}} dollars and take out 5% 
each year, {{{ x*( 1 - .05 )^n }}}, after n years, this is what you
have left, so after 10 yrs,
{{{ 50000*(  1 - .05 )^10 }}}
{{{ 50000*(.95)^10 }}}
{{{ 50000*.598737 }}}
{{{ 29936.847 }}}
In 10 yrs, the value of the fund is $29,936.85