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An investor buys $8,000 worth of a stock priced at $40 per share using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance margin. In 1 year the investor has interest payable and gets a margin call. At the time of the margin call the stock's price must have been ________.

Answer :

Answer:

$30.285

Explanation:

Data provided in the question:

Worth of stocks = $8,000

Stock price = $40

Number of stocks = [tex]\frac{8000}{40}[/tex] = 200

Initial margin = 50%

Broker charges = 6%

margin maintenance = 30% = 0.30

Now,

let At the time of the margin call the stock's price be 'x'

A margin call will occur if the ratio of Equity to the Market value will be 0.30 or less

thus,

0.30 = [tex]\frac{\textup{Equity}}{\textup{Market value}}[/tex]

here,

Equity = Market value - Initial margin - charges of broker

or

Equity = 200x - 0.50 × 8000 - 0.06 × (0.5 × 8000)

= 200x - 4000 - 240

Therefore,

0.30 = [tex]\frac{ 200x - 4000 - 240}{\textup{200x}}[/tex]

or

60x = 200x - 4,240

or

140x = 4,240

or

x = $30.285

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