On October $5,2022,$ you purchase a $$10,000$ Treasury$-$note that matures on August $15,2031($settlement occurs one day after

purchase, so you receive actual ownership of the bond on October $6,2022).$ The coupon rate on the Treasury$-$note is $4\mathrm{.}375$

percent and the current price quoted on the bond is $105\mathrm{.}250$ percent. The last coupon payment occurred on May $15,2022(144$

days before settlement$),$ and the next coupon payment will be paid on November $15,2022(40$ 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.

Note: For all requirements, do not round intermediate calculations. Round your answers to $3$ decimal places $($e$.$g$.,32\mathrm{.}161).$