On January $31,$ a company takes a long position in September futures on $3,200oz$ of gold at

$$1,\frac{227\mathrm{.}90}{o}z.$ The size of one contract is $100oz.$ The initial margin is $$22,08o$ per contract and the

maintenance margin is $$18,400$ per contract.

a$.$ How much money has to be deposited as the initial margin for the whole position?

b$.$ What is the smallest price change that would lead to a margin call?

c$.$ What should be the closing price of September gold futures on January $31,$ for the

exchange to withdraw $$39,040\mathrm{.}00$ from the margin account in the process of daily

settlement?

d$.$ What should be the closing price of September gold futures on January $31,$ for the

exchange to deposit $$21,632\mathrm{.}00$ to the margin account in the process of daily settlement?

e$.$ What amount $($if any$)$ would be required to be deposited by the company to the margin

account if the closing price of September gold futures on January $31$ were $$1,185\mathrm{.}6\frac{g}{o}z?$