$$ A speculator opens a long position in $40$ three$-$month E$-$mini S&P $500$ futures contracts at a futures price of $4,178\mathrm{.}50.$ The contemporaneous S&P $500$ Index value is $4,122\mathrm{.}40.$ a$.$ What is the value of the margin the speculator posts? b$.$ A few days later the futures price closes at $4,166\mathrm{.}15$; what is the value of the speculator$$s margin account? c$.$ If the speculator closes out the long position at a futures price of $4,159\mathrm{.}20$ what is the speculator$$s total profit$/$loss and the return on the speculator$$s investment? $$