Bill Gates has decided to take a short position in Tesla stock at $$1,000$ per share. He sells $100$ shares short at $$1,000$ per share. The following information applies for short sales:

IMR $=50\%$ MMR $=30\%$

d$)$ How much does Bill have to deposit in his account after taking the short position? Show a balance sheet of the account after the short sale e$)$ At what price would Bill double the value of his investment? $(2$ points$)$

f$)$ By what percentage would the price have to rise for Bill to be subject to a margin call? $(1$ point$)$