In January $2019,$ Mr$.$ Tom McInish won a prize of $ $900,000.$ Tom decided to sit on his money waiting for a good investment chance. For the last few years, Tom has been educating himself about the stock market. Tom heard a lot of investment professionals talking about making money by investing in new stocks offered to the public at initial public offerings $($IPOs$).$ So$,$ Tom is waiting for a good IPO to jump into the market. Tom started to learn about an upcoming IPO of an automobile company that so many people believe will change the future of the industry in the US and globally, that$$s Green Motors $($GRMT$).$ Tom likes this new company so much and is ready to start his investment journey once the stock goes public on Dec $29$th$,2019.$

$$ Tom was not able to purchase the stock at the IPO price of $$10.$ However, he purchased the shares in the secondary market for $$15$ per share on January $1$st$,2020.$ His account manager is also very positive about GRMT$,$ so she advised him to use the maximum allowed margin to maximize his returns from this great investment opportunity. Tom$$s broker's initial margin requirement is $60\%$ and she charges an interest rate of $5\%.$

$1)$ Jan $2020,$ he invested all his money $($$$900,000)$ in this stock, how much money will Tom borrow from his broker to use the entire margin in this transaction?

a$)$ $$900,000$ b$)$ $$300,000$ c$)$ $$600,000$ d$)$ $$1500,000$ e$)$ $$540,000$

$2)$ How many shares did he purchase if he used the entire allowed margin?

a$)90,000$ shares b$)30,000$ shares c$)15,000$ shares d$)100,000$ shares e$)60,000$ shares

$3)$ What is the minimum initial margin requirement as specified by the Federal Reserve system? a$)70\%$ b$)50\%$ c$)60\%$ d$)40\%$ e$)45\%$