You sell short $300$ shares of ZT Corp. at $$230$ per share. This transaction requires a $55\%$ percent margin.

a$.$ What is the initial margin position?

b$.$ Assume the price of ZT increases to $$290$ per share. If the minimum maintenance margin requirement is $30\%$ will you receive a margin call? Why? Why not? Explain.

c$.$ What is your rate of return?

d$.$ Calculate the price that will trigger a margin call.