```Question 609833
You can do this the long way without a formula
After 1 year:
{{{ 500 + .05*500 }}} in savings account
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After 2 years:
{{{ 500 + .05*500 + .05*( 500 + .05*500 ) }}}
Here's the trick: factor out {{{ 500 + .05*500 }}}
{{{ ( 500 + .05*500 )*( 1 + .05 )
Now factor out {{{ 500 }}} from the 1st term:
{{{ 500*( 1 + .05 )*( 1 + .05 ) }}}
{{{ 500*( 1 + .05 )^2 }}}
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After 3 years:
{{{ 500*( 1 + .05 )^2 + .05*( 500*( 1 + .05 )^2) }}}
Now factor out {{{ 500*( 1 + .05 )^2 }}}
{{{ 500*( 1 + .05 )^2 *( 1 + .05 ) }}}
{{{ 500*( 1 + .05 )^3 }}}
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As you can see, the  formula is {{{ 500*( 1 + .05 )^n }}}
where {{{ n }}} is the number of years
After {{{ 10 }}} years,
{{{ A = 500* 1.05^10 }}}
{{{ log( A ) = log( 500 ) + 10*log( 1.05 ) }}}
{{{ log( A ) = 2.6989 + 10*.02119 }}}
{{{ log ( A ) = 2.9108 }}}
{{{ A = 10^2.9108 }}}
{{{ A = 814.33 }}}
After 10 years, there is \$814.33 in the account
check:
{{{ 814.33 = 500*1.05^10 }}}
{{{ 814.33/500 = 1.05^10 }}}
{{{ 1.629 = 1.629 }}}
OK

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