Question 1042378
Maybe I can do it step by step
If I let {{{ t = 0 }}} ( no months have passed )
{{{ D(0) = 550 }}}
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{{{ t = 1 }}}
{{{ D(1) = 550 - .19*550 }}}
{{{ D(1) = 550*( 1 - .19 ) }}}
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{{{ t = 2 }}}
{{{ D(2) = 550*( 1 - .19 ) - .19*( 550*( 1 - .19 ) ) }}}
{{{ D(2) = 550*( 1 - .19 )*( 1 - .19 ) }}}
{{{ D(2) = 550*( 1 - .19 )^2 }}}
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This pattern continues, so the general formula is:
{{{ D(t) = 550*( 1 - .19 )^t }}}
{{{ D(t) = 550*.81^t }}}
I hope you see this. Each month 19% of the 
PREVIOUS months balance gets subtracted.