Need help with this margin maintenance question

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bullsofbayst

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Current price is $25 per share. You have 10k to invest. You borrow another 10k from your broker and invest 20k in the stock. If the maintenance margin is 30 percent at what price will a margin call first occur? The answer is 17.86
I’m just wondering how you go about calculating this.
 
Price margin call will occur = purchase price * [ (1-initial margin requirement) / (1-maintenance margin requirement) ]
If you start with $10,000 of your own money, and borrow another $10,000 from your broker and invest the full $20,000 then the initial margin requirement is 50%. The maintance margin requirement and purchase price are given to you so simply fill in the equation with the rest.
Price margin call will occur = $25 * [ (1-.5) / (1-.3) ]
= $25 * (0.5 / 0.7)
= $17.86
Hope this helps!
 
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