https://file.aiquickdraw.com/mathbot/file/17285139177219cqvol84.jpg

The equation in the image represents the Compound Annual Growth Rate (CAGR) formula. It is written as:

\[
\text{CAGR} = \left(\frac{1183.65}{1000}\right)^{\frac{1}{5}} - 1
\]

This formula is used to calculate the average annual growth rate of an investment over a certain number of years, assuming it grows at a steady rate.

To solve this:

1. First, calculate the ratio:
   \[
   \frac{1183.65}{1000} = 1.18365
   \]

2. Next, raise this ratio to the power of \(\frac{1}{5}\) (which is equivalent to taking the 5th root of the number):
   \[
   1.18365^{\frac{1}{5}} \approx 1.0345
   \]

3. Finally, subtract 1 from this value:
   \[
   1.0345 - 1 = 0.0345
   \]

Thus, the CAGR is approximately **0.0345**, or **3.45%**.

Would you like further details or explanations on this? Here are some follow-up questions you might consider:

1. What is the significance of CAGR in investment analysis?
2. How does CAGR compare to other growth metrics?
3. What are the assumptions underlying CAGR calculations?
4. Can CAGR be negative? What would it indicate?
5. How does the time period affect the CAGR result?

**Tip:** When calculating growth rates, ensure that all inputs (e.g., initial and final values) are accurate and consider the time period carefully for meaningful results.

Learn how to calculate the Compound Annual Growth Rate (CAGR) using the formula (1183.65 / 1000)^(1/5) - 1. This tutorial explains how to solve for CAGR with a detailed step-by-step approach, covering key concepts such as exponential growth and nth roots.

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