Suppose on July $1$ you take a short position in a June crude oil futures contract at $$50/$barrel

$($contract size $=1,000$ barrels$).$

a$.$ How much cash or risk$-$free securities would you have to deposit to satisfy an initial margin

requirement of $5\%?$

b$.$ Calculate the values of your commodity account on the following days, given the following

settlement prices:

$7/2$ $$50\mathrm{.}50$

$7/350\mathrm{.}75$

$7/550\mathrm{.}00$

c$.$ If the maintenance margin requirement specifies keeping the value of the commodity account

equal to $100\%$ of the initial margin requirement each day, how much additional cash would you

need to deposit or how much could you withdraw in your commodity account each day if you

choose to meet the minimum requirement?