Dee Trader opens a brokerage account and purchases $300$ shares of Internet Dreams at $$40$ per share. She borrows $$4,000$ from her broker to help pay for the purchase. The interest rate on the loan is $8\%.$ a$)$ What is the margin in Dee's account when she first purchases the stock? b$)$ If the share price falls to $$30$ per share by the end of the year, what is the remaining margin in her account? c$)$ If the maintenance margin requirement is $30\%,$ will she receive a margin call? d$)$ What is the rate of return on her investment?