Question $4(7$ marks$)$ The S&P $500$ spot is $2,929\mathrm{.}67$ and it is expected to pay a dividend yield of $3\%.$ The risk$-$free rate is $4\%$ per annum continuously compounded. Each contract is on $$250$ times the futures price.

$($a$)$ What is the theoretical $6-$month futures price? $(3$ marks$)$

$($b$)$ The $6-$month futures price is $3,000.$ Is there an arbitrage? If so$,$ show how we can benefit from it$?$ Show all details. $(4$ marks$)$