What is the duration of a $4-$year bond with an annual coupon rate of $9\%?$ Its value at maturity is $$1,000,$ the current bond price is $$1,103\mathrm{.}96,$ and the yield to maturity is $6\%.$ The present values of cash flows from Year $1$ through Year $4$ are $$84\mathrm{.}91,$$$80\mathrm{.}10,$$$75\mathrm{.}57,$ and $$863\mathrm{.}38.$

$3\mathrm{.}56$

$3\mathrm{.}23$

$4\mathrm{.}1$

$2\mathrm{.}44$