Question 761805
Let {{{ P }}} = amount deposited now
Let {{{ A }}} = the current savings
After 1st year,
{{{ A = P + .08P }}}
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After 2nd year,
{{{ A = ( P + .08P ) + .08*( P + .08P ) }}}
{{{ A = ( P + .08P )*( 1 + .08 ) }}}
{{{ A = P*( 1 + .08 )*( 1 + .08 ) }}}
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After 3rd year,
{{{ A =  P*( 1 + .08 )*( 1 + .08 ) + .08*( P*( 1 + .08 )*( 1 + .08 ) ) }}}
{{{ A = P*( 1 + .08 )*( 1 + .08 )*( 1 + .08 ) }}}
{{{ A = P*( 1 + .08 )^3 }}}
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So, this is the general rule:
{{{ A = P*( 1 + .08 )^t }}}
where {{{t }}} = the number of years since initial deposit
given:
{{{ A = 150000 }}}
{{{ t = 18 }}}
{{{ 150000 = P*( 1 + .08 )^18 }}}
{{{ 150000 = P*1.08^18 }}}
{{{ 150000 = 3.996P }}}
{{{ P = 37537.35 }}}
$37,537.35 needs to be deposited now
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Rate = 11%
{{{ 150000 = P*1.11^18 }}}
{{{ 150000 = 6.544P }}}
{{{ P = 22923.33 }}}
$22,923.33 needs to be deposited now