$6$

$(10$ points total$)$ Consider a deferred interest bond with a face value of $$1000,$ maturing in exactly $10$ years, with an annual yield to maturity of $9\%.$ The coupon rate is $8\%$ simple interest per year, with all interest accrued and paid at maturity.

a$)(5$ points$)$ Calculate the bond's modified duration $($in absolute value$),$ and interpret what it means.