Question $2(8$ marks$)$ General Mills stock sells at $$44\mathrm{.}46$ and is expected to pay dividends of $$0\mathrm{.}6$ in $3,6,9$ and $12$ months respectively. The risk$-$free rate is $5\%$ per annum continuously compounded for all maturities. We consider the $1-$year futures contract on General Mills.

$($a$)$ What is the theoretical $1-$year futures price? $(3$ marks$)$

$($b$)$ The $1-$year futures market price is $$46.$ Is there an arbitrage? If so$,$ how can we benefit from it$?$ Show all details. $(4$ marks$)$

$($c$)$ Based on the futures market price in part $($b$),$ what is the value of a short futures contract on General Mills $6$ months from now if the futures price in $6$ months is $44$$$?(1$ mark$)$