Math Problem Statement

For the following stock investment, find (a) the total purchase price, (b) the total dividend amount, (c) the capital gain or loss, (d) the total return, and (e) the percentage return.

Solution

Here is the breakdown of the problem and its solution:

Problem Setup:

  • Number of shares: 4040
  • Purchase price per share: 3030
  • Dividend per share: 11
  • Sale price per share: 6767

We need to calculate the following:

(a) Total Purchase Price:

Total Purchase Price=Number of Shares×Purchase Price per Share\text{Total Purchase Price} = \text{Number of Shares} \times \text{Purchase Price per Share} Total Purchase Price=40×30=1200\text{Total Purchase Price} = 40 \times 30 = 1200

(b) Total Dividend Amount:

Total Dividend Amount=Number of Shares×Dividend per Share\text{Total Dividend Amount} = \text{Number of Shares} \times \text{Dividend per Share} Total Dividend Amount=40×1=40\text{Total Dividend Amount} = 40 \times 1 = 40

(c) Capital Gain or Loss:

Capital Gain or Loss=(Sale Price per SharePurchase Price per Share)×Number of Shares\text{Capital Gain or Loss} = (\text{Sale Price per Share} - \text{Purchase Price per Share}) \times \text{Number of Shares} Capital Gain or Loss=(6730)×40=37×40=1480\text{Capital Gain or Loss} = (67 - 30) \times 40 = 37 \times 40 = 1480

(d) Total Return on Investment:

Total Return=Capital Gain or Loss+Total Dividend Amount\text{Total Return} = \text{Capital Gain or Loss} + \text{Total Dividend Amount} Total Return=1480+40=1520\text{Total Return} = 1480 + 40 = 1520

(e) Percentage Return:

Percentage Return=(Total ReturnTotal Purchase Price)×100\text{Percentage Return} = \left( \frac{\text{Total Return}}{\text{Total Purchase Price}} \right) \times 100 Percentage Return=(15201200)×100=1.2667×100127%\text{Percentage Return} = \left( \frac{1520}{1200} \right) \times 100 = 1.2667 \times 100 \approx 127\%


Final Answers:

  1. (a) Total Purchase Price: 12001200
  2. (b) Total Dividend Amount: 4040
  3. (c) Capital Gain or Loss: 14801480
  4. (d) Total Return: 15201520
  5. (e) Percentage Return: 127%127\%

Would you like further explanation on any part?
Here are 5 questions for exploration:

  1. How is the concept of dividend yield related to this problem?
  2. What happens to percentage return if the purchase price is doubled?
  3. How do transaction fees affect the calculation of returns?
  4. What is the impact of higher dividends on total return?
  5. How is percentage return used to compare different investments?

Tip: Always account for additional costs like brokerage fees for a more realistic return calculation!

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Math Problem Analysis

Mathematical Concepts

Investment Analysis
Stock Returns
Percentage Calculation

Formulas

Total Purchase Price = Number of Shares * Purchase Price per Share
Total Dividend Amount = Number of Shares * Dividend per Share
Capital Gain or Loss = (Sale Price per Share - Purchase Price per Share) * Number of Shares
Total Return = Capital Gain or Loss + Total Dividend Amount
Percentage Return = (Total Return / Total Purchase Price) * 100

Theorems

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Suitable Grade Level

Grades 10-12