Question $4(15$ marks$)$

An investor authorizes the broker to buy $4$ silver futures contracts at the beginning

of Day $1.$ Suppose the contract size of each contract is $100$ ounces and the futures

price is $$\frac{23}{?}$ ounce at the beginning of Day $1.$ The initial margin is $$110$ per

contract, and maintenance margin is $$80$ per contract. Assume that $(1)$ over the

next $5$ trading days, the futures contract does not expire, and the futures position is

not closed $($either by investor or broker$)$; $(2)$ no interest is paid to the margin

account; $(3)$ no fund is withdrawn from the margin account, and the minimum

required amount of top$-$up is made upon every margin calls. The settlement price at

the end of each day is given in the following table.

Table $4$: Daily Settlement Prices $($per ounce$)$

$($a$)(3$ marks$)$ What is the total initial margin to be deposited to open the

margin account?

$($b$)(6$ marks$)$ What are the daily gains at the end of each day from Day $1$ to Day

$5?$

$($c$)(6$ marks$)$ What is the margin account balance at the end of Day $5?$