Investor short sells 100 shares of a stock for 20 per share

Investor short sells 100 shares of a stock for $20 per share. The initial margin is 50% and the maintenance margin is 30%. The price of the stock rises to $28 per share. What is the margin, and will there be a margin call? If yes at what price?

Solution

100 Shares x $20 = $2,000
$2,000 x 0.50 = $1,000 Initial Loan Value

100 Shares x $28 = $2,800

Maintenance Margin =[ (Shares Price) - Initial Loan Value] / (Shares Price)

0.30 = (100p - $1,000)/100p
30p = 100p - 1,000
0 = 70p - 1,000
1,000 = 70p

P = 14.2857 rounds to 14.29

Thanks