$3.$ A $\backslash (\backslash$$ $5\backslash )-$year bond that pays a $\backslash (6\backslash \%\backslash )$ coupon annually has a face value of $\backslash (\backslash$$ $1,000\backslash ).$ You use this face value as collateral to create a $\backslash (\backslash$$ $500\backslash )$ floater $($paying SOFR, call this rate S$)$ and a $\backslash (\backslash$$ $500\backslash )$ inverse floater. The collateral bond currently sells for $\backslash (\backslash$$ $1,234\backslash ).$ a$)$ What are the coupon payments for the floater and the inverse floater? b$)$ What is the duration of the collateral bond? $($Hint: solve for ytm first$)$ c$)$ Given your answer to part b$,$ what is the duration of the inverse floater? $($hint: construct a weighted portfolio$)$