a$)$Suppose that the price of a bond futures contract that settles in three months is $105$ and the price of the underlying bond is $98.$ The underlying bond has a coupon rate of $8\%,$ par value of $100,$ and the next coupon payment is to be made in six months. The borrowing rate is $7\mathrm{.}4\%$ per annum. If an investor implemented a cash and carry trade, what would the arbitrage profit be$?$

b$)$ Using information in part $($a$),$ what is the theoretical futures price?