Question $3(12$ marks$)$

A corporate bond has a face value of $$1,000,$ a $5\%$ annual coupon rate $($paid semi$-$annually$),$ and $5$ years remaining to maturity. The yield to maturity $($YTM$)$ is $6\%($compounded semi$-$annually$).$ Today is $60$ days into the current $180-$day coupon period.

$($Show your steps!$)$

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

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

c$.$ Calculate the clean price of this transaction in terms of dollars and in $32$nds$.$