Margin Account I $[15$ marks$]$

Stock $x$ is currently selling at $$10$ per share. You just bought $1,000$ shares with $$6,000$ and the remainder borrowed from your broker. The requirement for the initial margin and minimum margin is $40\%$ and $36\%$ respectively. The margin account charges an interest rate of $14\%$ EAR. Assume you need to pay off the loan in $1$ year.

$($a$)[3$ marks$]$ Immediately after the trade, there is no change in the stock price. What is the percentage return of your investment?

$3$

$($b$)[3$ marks$]$ Immediately after the trade, the stock price drops to $8\mathrm{.}25.$ What is the percentage return of your investment?

$($c$)[3$ marks$]$ Immediately after the trade, how low can the price fall before you receive a margin call?

$($d$)[3$ marks$]$ One year has passed, and now the stock price is $$11.$ What is the percentage return of your investment over the past year? $[$note: you need to pay off your loan at the end of the year.$]$

$($e$)[3$ marks$]$ One year has passed. How low can the price fall before you receive a margin call? $[$note: you need to pay off your loan at the end of the year.$]$