Compute the total and annual returns on the described investment.
Six years after buying 200 shares of XYZ stock for ​$70 per​ share, you sell the stock for $ 21 comma 800.

To compute the total and annual returns on your investment, we will follow these steps:

### 1. **Calculate the Initial Investment:**
You bought 200 shares at $70 per share:
\[
\text{Initial Investment} = 200 \times 70 = 14,000
\]

### 2. **Calculate the Total Return:**
You sold the shares for $21,800, so the total return is the difference between the selling price and the initial investment:
\[
\text{Total Return} = 21,800 - 14,000 = 7,800
\]

### 3. **Calculate the Total Return Percentage:**
To express the total return as a percentage of the initial investment:
\[
\text{Total Return Percentage} = \left( \frac{\text{Total Return}}{\text{Initial Investment}} \right) \times 100 = \left( \frac{7,800}{14,000} \right) \times 100 = 55.71\%
\]

### 4. **Calculate the Annualized Return:**
The investment was held for 6 years, so to calculate the annualized return, we use the formula for compound annual growth rate (CAGR):
\[
\text{Annual Return (CAGR)} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1
\]
Where:
- Final Value = $21,800
- Initial Value = $14,000
- $ n = 6 $ (years)

Substitute the values:
\[
\text{Annual Return} = \left( \frac{21,800}{14,000} \right)^{\frac{1}{6}} - 1 \approx \left( 1.5571 \right)^{\frac{1}{6}} - 1 \approx 1.0743 - 1 = 0.0743 \, \text{or} \, 7.43\%
\]

### Summary of Results:
- **Total Return**: $7,800 (55.71%)
- **Annualized Return**: 7.43%

Would you like more details on any part of this calculation?

### Follow-up questions:
1. What is the significance of total return versus annualized return in evaluating an investment?
2. How would the returns change if the holding period was shorter or longer?
3. What are the effects of dividends on the total and annualized returns?
4. Can you explain how compounding influences the annualized return?
5. What factors should you consider before reinvesting the proceeds of a sold investment?

**Tip**: The annualized return (CAGR) is useful for comparing investments held for different periods, as it smooths out fluctuations.

Compute the total and annual returns on the described investment. Six years after buying 200 shares of XYZ stock for $70 per share, you sell the stock for $21,800.

Learn how to compute the total and annual returns for a stock investment. This example involves buying 200 shares of XYZ stock for $70 per share and selling them for $21,800 after six years. The solution covers key concepts like total return, percentage return, and annualized returns using the CAGR formula. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation