Q$8($c$)$ Suppose you notice mispricing in the futures market. The S&B stock index has a spot value of $185\mathrm{.}00$ now. S&B futures contracts are settled in cash, and underlying contract values are determined by multiplying $100$ times the index value. The current annual risk$-$free interest rate is $6\mathrm{.}0$ percent.

$($i$)$ Calculate the theoretical price of the futures contract expiring six months from now, using the cost$-$of$-$carry model. Show your calculations.

$(5$ marks$)$

$($ii$)$ The total $($round$-$trip$)$ transaction cost for trading a futures contract is $15\mathrm{.}00.$ Calculate the lower bound for the price of the futures contract expiring six months from now. Show your calculations.

$(5$ marks$)$