An investor opens a margin account with a discount broker. The initial margin requirement is $50\%.$ The maintenance margin is $30\%.$ The investor intends to buy $1,000$ shares of XYZ at $$40.$ An interest rate on the margin loan is $4\%$ per year. The stock does not pay any dividends.

a$)$ How much money must the investor deposit?

b$)$ Assuming the investor deposits $$30,000($NOT the amount you calculated in part a and buys the shares. How far could the stock price fall before the investor would get a margin call?

c$)$ Assuming the investor receives a margin call. How much money must the investor deposit to avoid the liquidation actions by the broker?

d$)$ Assume in one year, the stock's price decreases to $$14\mathrm{.}29$ per share, and the investor receives a margin call. Instead of depositing the amount calculated in part $($c$)$ the investor sells the shares. What is the rate of return realized by the investor?

$1$

e$)$ Assume the investor has a cash account $($not a margin account$).$ Recalculate the rate of return in part $($d$).$

f$)$ Assume in one year, the stock's price increased to $$45,$ but the investor did not sell the shares. What is the buying power of the margin account?

g$)$ Assuming the situation described in part $($f$),$ how much can the investor withdraw in cash?

h$)$ Assuming the investor decides to short sale the stock $($instead of buying it$)$ and receives $$40$ per share. If he$/$she deposits the amount you calculated in part $($a$),$ how far can the stock price rise before the investor receives a margin call?