The problem describes a scenario where an investor purchases stock, borrows money to finance part of the purchase, and then the stock price falls. We are asked to calculate the remaining margin in the investor's account, the percentage margin, and the rate of return on the investment.

1. Problem Description

The problem describes a scenario where an investor purchases stock, borrows money to finance part of the purchase, and then the stock price falls. We are asked to calculate the remaining margin in the investor's account, the percentage margin, and the rate of return on the investment.

2. Solution Steps

a. The stock is purchased for 300 shares at $40 per share, totaling$12,

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0. b. The amount borrowed is $4,000, so the investor's initial equity or margin is $12,000 - $4,000 = $8,

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0. c. The share price falls to $30, making the total value of the stock $30 * 300 = $9,

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0. d. The amount owed to the broker grows to $4,000 * 1.08 = $4,320 (due to interest).

e. The remaining margin in the investor's account is the current value of the stock minus the amount owed to the broker: $9,000 -$4,320 = $4,

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0. f. The percentage margin is calculated by dividing the remaining margin by the value of the stock: $4,680 / $9,000 = 0.52 = 52%.

g. The rate of return on the investment over the year is calculated as (Ending equity - Initial equity) / Initial equity. In this case, the ending equity is $4,680, and the initial equity is$8,

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$Rate of Return = (Ending Equity - Initial Equity) / Initial Equity$

$Rate of Return = ($4,680 - $8,000) /$8,000$

$Rate of Return = -$3,320 / $8,000$

$Rate of Return = -0.415$

$Rate of Return = -41.5$

3. Final Answer

The remaining margin in the investor's account is $4,

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0. The percentage margin is 52%.

The rate of return on the investment over the year is -41.5%.