Chris purchased $200$ shares of PTM stock $15$ months ago with $50\%$ margin at $$54$ a share. PTM currently trades at $$74$ a share. It peaked at $$80$ a share and Chris is getting nervous that his gains could diminish rapidly, so Chris enters a Stop$-$Limit order at $$72.$

Select each answer below that is TRUE based on these facts. To be clear, if you think only one answer is true, only mark one answer. If you think $2$ answers are true, mark both of them. If you think $3$ answers are true, mark all $3$ answers. And if you think all $4$ answers are true, mark all $4$ answers.

$($Each answer below is graded separately. If you mark a correct answer as correct, you get points. If you leave a correct answer unmarked, no points earned. If you mark an incorrect answer as correct you lose points. It's better to leave an answer unmarked if you are unsure than to mark an incorrect answer as correct.$)$

a$.$

PTM drops to $$70\mathrm{.}75,$ then rises to $$72\mathrm{.}30,$ and then drops again to $$69\mathrm{.}50.$ Chris's PTM stock sold at or near $$72$ and he is happy that he didn't keep the PTM stock any longer.

b$.$

PTM stock bounces back and Chris cancels his Stop$-$Limit order and instead places a market order to sell all $200$ shares of PTM stock and it sells at $$78.$ Assuming no interest charges on the margin, Chris realizes a long term capital gain of $$7,500.$

c$.$

PTM drops consistently, all the way down to $$69\mathrm{.}50.$ Much to Chris's surprise he still owns $200$ shares of PTM stock. He's pretty disappointed thinking his order would have sold his stock once it dropped below $$72.$

d$.$

Chris was able to buy the $200$ shares of PTM using only $$2700$ of his own money.