Consider a $6-$month futures contract on the S&P $500$ index. If the current value of the index

is $1,000,$ the dividend yield is $3$ percent per year continuously compounded, and the risk$-$free

rate of interest $($r$)$ is $4$ percent per year continuously compounded.

a$)$ What is the no arbitrage futures price?

b$)$ What should you do to take advantage of the arbitrage opportunity if the actual S&P $500$

index futures price is $$1,010?$