Question $2[20$ points$]$

Your broker requires an initial margin of $40\%$ and a maintenance margin of $20\%,$ both for short sales and for margin borrowing. Your initial capital in your brokerage account is CAD $500,000$ and the interest rate for margin loans is $6\%.$ The price of a share of RBC is CAD $50\mathrm{.}00.$

$($a$)$ How many shares of RBC could you maximally buy?

$($b$)$ Suppose you buy $20,000$ shares of RBC at the current price, show the initial Position. at what future price would you start receiving a margin call?

$($c$)$ Suppose you buy $20,000$ shares of RBC at the current price and, after a year, the price has fallen to CAD $48\mathrm{.}00.$ Show the new position. Will you receive margin call? What is your annual return?

$($d$)$ How many shares of RBC could you maximally short?

$($e$)$ Suppose you short $10,000$ shares of RBC at the current price, Show your position. at what future price would you receive a margin call?