Today is May $1.$ Mr$.$ Leonard B$.$ Ozo is a trust fund manager at Kalamazoo National Bank. Mr$.$ Ozo has excess cash which he wishes to invest for $60$ days. He decides the best deal going is to invest the funds in $$5$ million dollars $($face value$)$ of $180$ day commercial paper for the $60$ days. Hence the $180$ day commercial paper is bought today in the spot at a cost of $$4,768,750.$ To protect the investment, he decides to hedge the spot position with T$-$bill futures contracts which call for delivery of $90$ day T$-$bills. Given the data below determine:

a$)$ The correct number of contracts to hedge with and whether the appropriate position is a long or short hedge.

b$)$ The effective annual compound rate of return $($ytm$)$ earned on the investment with the hedge. Round the HPRs to $4$ decimal places$)$

c$)$ The effective annual rate savings $($cost$)$ in basis points due to the hedge. Was Mr$.$ Ozo glad he hedged? Why or why not?