Instructions: $(1)$ Do not show the calculation process. Provide your final answers only. $(2)$ Use four decimal places for your calculations. Show your answers by rounding the calculation results to two decimal places if the answers are in dollars. For example, if your calculation results in $$100\mathrm{.}1265,$ show your answer as $$100\mathrm{.}13.$ If you need to show your answers as a percent, take four decimal places from your calculation and convert them into a percent. For example, if your calculation results in $0\mathrm{.}4567,$ show $45\mathrm{.}67\%,$ not $45\mathrm{.}7\%$ or $46\%.$ To set your Texas Instrument BA II PLUS calculator at $4$ decimal places, press $[2$ND$]$ FORMAT $4[$ENTER$].$ Please follow the instructions for homework assignments on the syllabus.

Questions

Part I: Buying on Margin

Use the following information for questions $15.$

You open a brokerage account with Western Securities and purchases $200$ shares of ABC Company at $$60$ per share on the first business day of the year. You borrow $30$ percent of the purchase amount from your broker to help pay for the investment.

$1.$ What is the initial dollar margin?

$2.$ What is the initial percentage margin?

$3.$ If the maintenance margin is $30\%,$ how far could the stock price fall before you would get a margin call? Assume the price fall happens immediately.

$4.$ Assuming an interest rate on the margin loan of $5\%$ per year, what will be your rate of return $($ignoring dividends and taxes$)$ if the stock goes up by $20\%$ by year$$s end?

$5.$ Assuming an interest rate on the margin loan of $5\%$ per year, what will be your rate of return $($ignoring dividends and taxes$)$ if the stock goes down by $20\%$ by year$$s end?