A futures contract is available on a company that pays an annual dividend of $$5$ and whose stock is currently pricA futures contract is available on a company that pays an annual dividend of $$5$ and whose stock is currently priced at $$200.$ Each futures contract calls for delivery of $1,000$ shares of stock in one year, daily marking to market, an initial margin of $10\%$ and a maintenance margin of $5\%.$ The current Treasury bill rate is $8\%.$

$($a$)$ Given the above information, what should the price of one futures contract be$?$

$($b$)$ If the company stock decreases by $7\%,$ what will be$,$ if any, the change in the futures price?

$($c$)$ As a result of the company stock decrease, will an investor that has a long position in one futures contract of this company realize a gain or a loss? Why? What will be the amount of this gain or loss?

$($d$)$ What must the initial balance in the margin account be$?$ Following the stock decrease, what will be$,$ if any, the change in the margin account? Will the investor need to top up the margin account? If yes, by how much and why?

$($e$)$ Given the company stock decrease, what is the percentage return on the investor$$s position? Is it higher, equal or lower than the $7\%$ company stock decrease? Why? ed at $$200.$