Fifteen years after purchasing shares in a mutual fund for $5600 the shares are sold for ​$11300. Part 1:The the total return is 101.8​%. ​Part 2: The annual return is ____​%

To calculate the annual return, we use the formula for compound annual growth rate (CAGR), which is given by:

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

Where:
- Final Value = $11,300
- Initial Value = $5,600
- $ n = 15 $ years

Let's calculate this:

\[
\text{CAGR} = \left( \frac{11300}{5600} \right)^{\frac{1}{15}} - 1
\]

Now let's compute this.The annual return is approximately **4.79%**.

Would you like any further details or have any questions?

Here are 5 related questions you might consider:
1. How does the total return compare to the annual return?
2. What would the annual return be if the investment period was shorter, like 10 years?
3. How does the annual return change with different initial or final values?
4. What is the impact of inflation on the real annual return?
5. How does this annual return compare to average market returns?

**Tip:** When analyzing investments, it's important to distinguish between total return and annualized return, as the latter provides a better understanding of growth over time.

Fifteen years after purchasing shares in a mutual fund for $5600 the shares are sold for $11300. Part 1: The total return is 101.8%. Part 2: The annual return is ____%.

Learn how to calculate the annual return on a mutual fund investment held for 15 years. This problem demonstrates the use of the Compound Annual Growth Rate (CAGR) formula, showing how an initial investment of $5600 grows to $11300, resulting in an annual return of approximately 4.79%. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation