You are a financial analyst at a brokerage firm, and one of your clients, Sandra, a seasoned investor, is interested in short selling shares of TechGen Inc. The current market price of TechGen stock is $$80$ per share. Your client wants to short sell $300$ shares of TechGen Inc. Your brokerage firm has an initial margin requirement of $60\%$ and a maintenance margin requirement of $30\%.$

a$.$ Calculate the amount of cash or securities Sandra must put into her brokerage account to meet the initial margin requirement. $(1$ mark$)$

b$.$ Determine how high the price of TechGen stock can rise before your client receives a margin call, given the maintenance margin requirement. $(2$ marks$)$

$.$ How is margin trading different from short selling? $(2$ marks$)$