Answer: $19.05.

## Explanation To determine the price at which a margin call occurs, we need to calculate the **maintenance margin requirement** and find the stock price that triggers it. **Given:** - Initial deposit = $5,000 - Shares purchased = 300 - Purchase price = $30 per share - Maintenance margin = 30% **Step 1: Calculate total purchase value** Total purchase = 300 shares × $30/share = $9,000 **Step 2: Calculate loan amount (margin borrowed)** Loan amount = Total purchase - Initial deposit = $9,000 - $5,000 = $4,000 **Step 3: Calculate equity when price changes** Let P = stock price Equity = (300 × P) - $4,000 (market value minus loan) **Step 4: Maintenance margin formula** Maintenance margin = Equity / Market value ≥ 30% Equity / (300 × P) ≥ 0.30 **Step 5: Set up inequality** (300P - 4000) / (300P) ≥ 0.30 **Step 6: Solve for P** 300P - 4000 ≥ 0.30 × 300P 300P - 4000 ≥ 90P 300P - 90P ≥ 4000 210P ≥ 4000 P ≥ 4000/210 P ≥ 19.0476 **Step 7: Interpret result** The maintenance margin requirement is satisfied when P ≥ $19.05. When P < $19.05, equity/market value < 30%, triggering a margin call. **Therefore, the price below which the investor will first receive a margin call is $19.05.** **Verification:** At P = $19.05: - Market value = 300 × $19.05 = $5,715 - Equity = $5,715 - $4,000 = $1,715 - Equity ratio = $1,715 / $5,715 = 0.300 = 30% (exactly at maintenance margin) At P = $19.04: - Market value = 300 × $19.04 = $5,712 - Equity = $5,712 - $4,000 = $1,712 - Equity ratio = $1,712 / $5,712 = 0.2997 = 29.97% (< 30%, margin call) Thus, **Option A ($19.05)** is correct.

Author: LeetQuiz .