A$)$ Suppose that the price of a bond futures contract that settles in four months is $$101$ and the price of the underlying bond is $$98.$ The underlying bond has a coupon rate of $9\%,$ par value of $$100,$ and the next coupon payment is to be made in six months. The borrowing rate is $7\mathrm{.}2\%$ per annum. If an investor implemented a cash and carry trade, what would the arbitrage profit be$?$

B$)$ Suppose that instead of a futures price of $$101,$ the futures price is $$96.$ If an investor implemented a reverse cash and carry trade, what would the arbitrage profit be$?$

C$)$ What is the theoretical futures price?

D$)$ Demonstrate using a cash and carry trade that the theoretical futures price computed

in part $($c$)$ will produce no arbitrage profit