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$10$ points

On October $5,2019,$ you purchase a $$10,000$ T$-$note that matures on August $15,2031($settlement occurs two days after purchase, so you receive actual ownership of the bond on October $7,2019).$ The coupon rate on the T$-$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 $15,2019(145$ days before settlement$),$ and the next coupon payment will be paid on November $15,2019(39$ 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.

$($For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

Answer is complete but not entirely correct.

$\backslash$table$[[$a$.,$Accrued interest due,$$,561\mathrm{.}67$