Consider a $15$ year bond with a coupon rate of $4\mathrm{.}5\%$ and a YTM of $5\mathrm{.}2\%.$ The modified duration of this bond is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$

A$.9\mathrm{.}3$ years

B$.9\mathrm{.}8$ years

C$.10\mathrm{.}4$ years

D$.10\mathrm{.}9$ years