What is the average annual compound rate of return for a fund with the following values?

Fund price, beginning of year 1	 19.16
Fund price, end of year 3	 21.05
Annual distribution, year 1	 0.87
Annual distribution, year 2	 1.86
Annual distribution, year 3	 0.67

To calculate the **average annual compound rate of return** (CAGR), we need to account for both the price appreciation of the fund and the distributions made over the 3-year period.

The formula for the **CAGR** is:

\[
CAGR = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1
\]

Where:
- \(FV\) = final value of the investment (including the price at the end of the period and distributions)
- \(PV\) = initial value of the investment (price at the beginning of the period)
- \(n\) = number of years

### Step 1: Calculate the Total Final Value of the Investment (FV)
The final value of the investment should include the price at the end of year 3, plus all the distributions during the 3 years, assuming the distributions are reinvested.

So the **final value** is:

\[
FV = \text{Price at the end of Year 3} + \text{Distributions}
\]

Given:
- Initial price \(PV = 19.16\)
- Final price \(FV_{\text{price}} = 21.05\)
- Annual distributions: \(D_1 = 0.87\), \(D_2 = 1.86\), \(D_3 = 0.67\)

The distributions must be added to the final value. Assuming the distributions are treated as part of the return (i.e., they are reinvested), we can sum them up:

\[
FV = 21.05 + (0.87 + 1.86 + 0.67) = 21.05 + 3.40 = 24.45
\]

### Step 2: Calculate the CAGR

Now we can plug the values into the CAGR formula:

\[
CAGR = \left( \frac{24.45}{19.16} \right)^{\frac{1}{3}} - 1
\]

Let's calculate that.The average annual compound rate of return (CAGR) for the fund over the 3-year period is approximately **8.47%**.

Would you like more details, or do you have any questions?

Here are 5 related questions to deepen your understanding:
1. How does reinvesting distributions affect the overall return of an investment?
2. What is the difference between simple return and compound return?
3. How would the CAGR change if one year had a negative distribution?
4. How can you compare CAGRs across different funds or investments?
5. What other metrics can be used to assess the performance of a fund?

**Tip**: The CAGR smooths out returns over multiple periods, providing a steady rate of return even if the annual returns are volatile.

What is the average annual compound rate of return for a fund with the following values?
Fund price, beginning of year 1: 19.16
Fund price, end of year 3: 21.05
Annual distribution, year 1: 0.87
Annual distribution, year 2: 1.86
Annual distribution, year 3: 0.67

Learn how to calculate the average annual compound rate of return (CAGR) for a fund with given starting and ending prices, and annual distributions over a 3-year period. This guide includes step-by-step instructions using the CAGR formula and covers key concepts such as reinvested distributions and investment growth.

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