Suppose you sell short $200$ shares initially trading for $$50$ per share. Your initial margin requirement is $50\%$ of the value of the short positions. You receive no interest for the funds placed in your margin account. $1.$ How much do you need to contribute to your margin account? $2.$ After $1$ year, what will be your rate of the return considering the following stock prices? $$40,$ $$50,$ $$60.3.$ How high can the price of the stock go before you get a margin call if the maintenance margin is $30\%$ of the value of the short position?