An investor has a portfolio containing $1,000$ worth of a $3-$year bond with a modified duration of $2\mathrm{.}7$; $4,000$ worth of a $5-$year bond with a modified duration of $4\mathrm{.}6$; and $5,000$ worth of a $6-$year bond with a modified duration of

$5\mathrm{.}5.$ Find the modified duration of the entire portfolio.