Consider a $5-$year semiannual payment floating$-$rate security whose coupon rate is determined as:

reference rate $+45$ basis points

The current reference rate is $8\%$ and bond's price is $98\mathrm{.}5.$

$(1)$ What is the current coupon rate? $(1$ points$)$

$(2)$ What is the required yield of the floating$-$rate bond? $(5$ points$)$

$(3)$ What is the discount margin of the floating$-$rate bond? $(2$ points$)$