$4.$ On October $5,2022,$ you purchase a $\backslash (\backslash$$ $10,000\backslash )$ T$-$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 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 $15,2022(144$ days before settlement$),$ and the next coupon payment will be paid on November $15,2022(40$ days from settlement$).($LG $6-2)$

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

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

Supplemental Problem

Bond Quotation. Use the following February $11,2002,$ Wall Street Journal quotation for AT$\backslash$&T Corp. Which of the following statement is false?

$(1)$ The closing price of the bond with the shortest time to maturity is $\backslash (\backslash$$ $1,000\backslash ).$

$(2)$ The annual coupon for the bond maturing in $2018$ is $\backslash (\backslash$$ $90\backslash ).$

$(3)$ The price on the day before this quotation $($February $9)$ for the AT$\backslash$&T bond maturing in $2024$ is $\backslash (\backslash$$ $1,075\backslash )$ per bond contract.

$(4)$ The current yield on the AT$\backslash$&T bond maturing in $2004$ is $7\mathrm{.}125$ percent.

$(5)$The AT$\backslash$&T bond maturing in $2004$ has a yield to maturity of less than $7\mathrm{.}125$ percent.