Question 1076511
After the 1st year, you have:
{{{ 1000*( 1 + .05 )^0 = 1000 }}}
The 2nd year you have:
{{{ 1000*( 1 + .05 )^1 }}}
Then the 3rd year you have:
{{{ 1000*( 1 + .05 )^1 + .05*( 1000*( 1 + .05 )^1 ) }}}
If you get this next step, then you get the whole thing.
Factor out {{{ 1000*( 1 + .05 )^1 }}}
{{{ 1000*( 1 + .05 )^1 *( 1 + .05 )^1 }}}
{{{ 1000*( 1 + .05 )^2 }}}
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And if you repeat this for 18 years, you get:
{{{ 1000*( 1 + .05 )^17 }}}
{{{ 1000*1.05^17 }}}
{{{ 1000*2.292018 = 2292.02 }}}
$2,292.02 saved after 18 years
Feel free to get a 2nd opinion on  this