You purchase $500$ shares of Compucon for $$120$ per share using a margin account. This transaction requires a $45\%$ percent margin.

a$.$ What is the initial margin position?

b$.$ Assume the price of Compucon declines to $$90$ per share. If the minimum maintenance margin requirement is $25\%$ 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.