You want to purchase GM shares at $50 from your broker using as little of your own money as possible. If initial margin is 50% and you have $8,000 to invest, how many shares can you buy?

Question

BlackTom AI · Accepted Answer

Initial margin requirement of 50% means you must provide half of the total purchase cost in your own cash; the broker can finance the other half. With $8,000 available, you can buy shares whose total cost equals cash / margin = 8,000 / 0.50.

Step-by-step reasoning and calculations:
1. Total purchase capacity = available equity ÷ initial margin
   = 8,000 ÷ 0.50
   = 16,000 dollars.
2. Share price = $50, so number of shares = total purchase capacity ÷ price per share
   = 16,000 ÷ 50
   = 320 shares.

Why this is correct:
- For 320 shares at $50 each the total cost is 320 × $50 = $16,000. With a 50% initial margin you must supply 50% of $16,000 = $8,000 in cash, which exactly equals your available funds. Thus 320 is the maximum whole number of shares you can buy without exceeding your $8,000 equity.

Why the other options are incorrect:
- 230 shares → cost = 230 × $50 = $11,500; required equity = 50% × $11,500 = $5,750. This uses less than your $8,000 (not maximal).
- 340 shares → cost = 340 × $50 = $17,000; required equity = $8,500, which exceeds your $8,000 (not allowed).
- 480 shares → cost = 480 × $50 = $24,000; required equity = $12,000, well above your funds (not allowed).
- 250 shares → cost = 250 × $50 = $12,500; required equity = $6,250, under your limit (not maximal).

Conclusion: therefore the correct and maximal number of shares you can buy given a 50% initial margin and $8,000 is 320 shares, matching the provided answer.

You want to purchase GM shares at $50 from your broker using as little of your own money as possible. If initial margin is 50% and you have $8,000 to invest, how many shares can you buy?单项选择题

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