You decide to open a margin account with your broker. You deposit $30,000 in your account. In addition, you borrow $30,000 from your broker and purchase 600 shares of XYZ corporation at $100 per share. As soon as you buy the stock, it drops to $88 per share.

a) What is your margin rate after the stock price drop to $88 per share?

b) If the stock drops further to $80 per share, how much money will you need to deposit in your account to bring the margin rate up to 40%?

c) Assume the stock price again drops to $80 per share. If you refuse to deposit any extra money into your account, and your broker is forced to sell off shares in your account to bring the margin back up to 40%, how many shares must the broker sell?

d) What is the rate of return in your margin position if XYZ is selling after one year at (i) $110, (ii) $90? 

What is the relation between your return and the percentage change in the price of XYZ?