Margin Call at Stock Price?

CFA Level I
#1

CFAI Mock Example Q83 Morning Exam

Trader buys 500 shs on margin at $36/shs

Leverage ratio: 1.66

Maintenance margin requirement: 30%

What is the stock price that margin call will occur at?

I read the answer but I don’t understand the intuition. Could you guys please explain how I would be able to go through it in my mind without using the formula? Thanks!

#2

1/1.66= .6024 = equity in the position. Don;t know that you’re going to get away without a formula here, but I prefer this equation to the CFAI books:

Call Price = Purchase Price*((1-initial equity)/(1-maintenance margin%))

Call Price = 36 X ((1-.60) / (1-.30)) = 36 X .57 = $20.57