Mary Reid invested $10,000 and borrowed $10,000 to purchase shares in JP Morgan Chase. At the time of her investment, Chase was selling for $141 a share.

    If Mary paid a commission of $12, how many shares could she buy if she used only her own money and did not use margin?Note: Round your final answer to 1 decimal place.

    Note: Round your final answer to 1 decimal place.
    If Mary paid a commission of $20, how many shares could she buy if she used her $10,000 and borrowed $10,000 on margin to buy Chase stock?

    Note: Round your final answer to 1 decimal place.
    Assume Mary did use margin to buy her Chase stock. Also, assume she paid another $20 to sell her stock and sold the stock for $157 a share. How much profit did she make on her Chase stock investment?

    Note: Round intermediate calculations to 1 decimal place. Round your final answer to 2 decimal places.


Let's break down each part of the problem step-by-step:

### 1. **Number of Shares without Margin (using $10,000 and a $12 commission)**

If Mary uses only her own money and does not use margin, she has $10,000 to invest. Subtracting the $12 commission, the amount she has available to buy shares is:

\[
10,000 - 12 = 9,988
\]

The cost per share is $141, so the number of shares she can buy is:

\[
\text{Number of shares} = \frac{9,988}{141} \approx 70.9 \, \text{shares}
\]

So, Mary can buy **70.9 shares** with her own money.

---

### 2. **Number of Shares with Margin (using $10,000 of her own money + $10,000 borrowed, and a $20 commission)**

If Mary uses both her own money and the borrowed money, she has a total of:

\[
10,000 + 10,000 = 20,000
\]

Subtracting the $20 commission, the amount she has available to buy shares is:

\[
20,000 - 20 = 19,980
\]

The cost per share is $141, so the number of shares she can buy is:

\[
\text{Number of shares} = \frac{19,980}{141} \approx 141.7 \, \text{shares}
\]

So, Mary can buy **141.7 shares** using margin.

---

### 3. **Profit Calculation when Selling Shares**

Mary bought 141.7 shares (from Part 2) using margin. She paid an initial commission of $20 when buying and an additional $20 commission when selling.

The selling price is $157 per share, so the total amount she receives is:

\[
141.7 \times 157 = 22,238.9
\]

After subtracting the $20 selling commission:

\[
22,238.9 - 20 = 22,218.9
\]

The amount borrowed was $10,000, which she needs to repay. So, her net amount after repaying the borrowed amount is:

\[
22,218.9 - 10,000 = 12,218.9
\]

### **Initial Investment**:
Mary's initial investment was $10,000 of her own money.

### **Profit**:
\[
12,218.9 - 10,000 = 2,218.9
\]

Therefore, Mary made a profit of **$2,218.90**.

---

Let me know if you'd like more details or have further questions. Here are 5 related questions for exploration:

1. How would the profit change if the stock sold for $150 per share instead of $157?
2. What if Mary did not use any margin and invested $10,000 without borrowing?
3. What would happen if the stock price dropped to $120 instead of increasing?
4. How does the commission fee affect the number of shares Mary can buy?
5. What is the percentage return on her investment?

**Tip**: When calculating profits using margin, always remember to subtract the borrowed amount to determine the true gain or loss.

Mary Reid invested $10,000 and borrowed $10,000 to purchase shares in JP Morgan Chase. At the time of her investment, Chase was selling for $141 a share. If Mary paid a commission of $12, how many shares could she buy if she used only her own money and did not use margin? Note: Round your final answer to 1 decimal place. If Mary paid a commission of $20, how many shares could she buy if she used her $10,000 and borrowed $10,000 on margin to buy Chase stock? Note: Round your final answer to 1 decimal place. Assume Mary did use margin to buy her Chase stock. Also, assume she paid another $20 to sell her stock and sold the stock for $157 a share. How much profit did she make on her Chase stock investment? Note: Round intermediate calculations to 1 decimal place. Round your final answer to 2 decimal places.

Learn how to calculate the number of shares Mary Reid could buy with a $10,000 investment in JP Morgan stock, both with and without margin, including commission fees. Also, discover how to compute her profit when selling the stock at a higher price. This detailed solution covers essential financial math concepts like arithmetic, profit, and investment calculations, suitable for students in Grades 10-12.

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