The margin requirement on the S&P $500$ futures contract is $10\%,$ and the stock index is currently $1,800.$ Each contract has a multiplier of $$50.$

Required:

a$.$ How much margin must be put up for each contract sold?

b$.$ If the futures price falls by $2\%$ to $1,764,$ what will happen to the margin account of an investor who holds one contract? $($Input the amount as a positive value.$)$

c$-1.$ What will be the investor's percentage return based on the amount put up as margin? $($Negative value should be indicated by a minus sign. Round your answer to $2$ decimal places.$)$

c$-2.$ What would be the current cash balance in the margin account?