Problem $1$

On October $5,2013,$ you purchase a $$10,000$ T$-$note that matures on August $15,2024($settlement occurs two days after purchase so you receive actual ownership of the bond on October $7,2013).$ The coupon rate on the T$-$note is $4\mathrm{.}375\%$ and the current price quoted on the bond is $105$:$08.$ The last coupon payment occurred on May $15,2013(145$ days before settlement$),$ and the next coupon payment will be paid on November $15,2013(39$ days from settlement$).$

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

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