Compute the total and annual returns on the following investment.

Ten years after purchasing shares in a stock for $6200, the shares are sold for $12,400

The total return is 
 %  Round answer to nearest percent

The annual return is 
 % Round answer to nearest 0.1 percent

### Step 1: Compute the Total Return

The total return formula is:

\[
\text{Total Return} = \frac{{\text{Final Value} - \text{Initial Value}}}{{\text{Initial Value}}} \times 100
\]

- Initial Value = $6200
- Final Value = $12,400

Substitute these values:

\[
\text{Total Return} = \frac{{12,400 - 6200}}{{6200}} \times 100
\]

Now, calculate the total return.

\[
\text{Total Return} = \frac{{6200}}{{6200}} \times 100 = 100\%
\]

Thus, the total return is **100%**.

### Step 2: Compute the Annual Return

The annual return is calculated using the formula for compound annual growth rate (CAGR):

\[
\text{Annual Return} = \left( \frac{{\text{Final Value}}}{{\text{Initial Value}}} \right)^{\frac{1}{n}} - 1
\]

Where:
- $ n $ is the number of years (in this case, 10 years),
- Initial Value = $6200,
- Final Value = $12,400.

Now, calculate the annual return:

\[
\text{Annual Return} = \left( \frac{{12,400}}{{6200}} \right)^{\frac{1}{10}} - 1
\]

Let's compute this.- The total return is **100%**.
- The annual return is approximately **7.2%**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How does compound interest differ from simple interest when calculating returns?
2. What is the impact of inflation on investment returns over 10 years?
3. How would annual returns differ if the time period was reduced to 5 years?
4. What other metrics are useful in evaluating long-term investments?
5. How does risk factor into expected investment returns?

**Tip:** The compound annual growth rate (CAGR) is useful to compare investments with different time horizons.

Compute the total and annual returns on the following investment.

Ten years after purchasing shares in a stock for $6200, the shares are sold for $12,400

The total return is % (Round answer to nearest percent)

The annual return is % (Round answer to nearest 0.1 percent)

Learn how to compute total and annual returns for a 10-year investment. This problem involves calculating the total return of 100% and an annual return of approximately 7.2% using key formulas like total return and compound annual growth rate (CAGR). Suitable for students in Grades 10-12.

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