Question 982141
Let {{{ V }}} = it's original value
Let {{{ V/2 }}} = it's final value
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Let {{{ n }}} = number of years until
{{{ V }}} becomes {{{ V/2 }}}
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{{{ V/2 = V*( 1 - .08 )^n }}}
Divide both sides by {{{ V }}}
{{{ 1/2 = ( 1 - .08 )^n }}}
{{{ 1/2 = .92^n }}}
{{{ log( .5 ) = n*log( .92 ) }}}
{{{ n = log( .5 ) / log( .92 ) }}}
{{{ n = .30103 / .03621 }}}
{{{ n = 8.3134 }}}
At the end of the 8th year, the value will
be less than 1/2 of it's original value
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check:
{{{ 1/2 = .92^n }}}
{{{ .5 = .92^8.3134 }}}
{{{ .5 = .49998 }}}
close enough