Question $4(8$ marks$)$

On June $15,2018,$ you purchase a $$100,000$ T$-$note that matures on Nov $15,2024($settlement occurs two days after purchase, so you receive actual ownership of the bond on June $17,2018).$ The coupon rate on the T$-$note is $5\mathrm{.}4\%$ and the current price quoted on the bond is $108$:$08.$ The last coupon payment occurred on May $15,2018,$ and the next coupon payment will be paid on Nov $15,2018.$

a$.$ Calculate the accrued interest due to the seller from the buyer at settlement.

b$.$ Calculate the dirty price of this transaction.