Calculate the compound growth rate given the following annual growth rates.

Note: Round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.
5.25% 	6.35% 	4.55% 	4.95% 	7.95%

To calculate the **compound growth rate (CAGR)** from a set of annual growth rates, we use the geometric mean formula.

1. Convert the percentage growth rates to their decimal form.
   - 5.25% = 0.0525
   - 6.35% = 0.0635
   - 4.55% = 0.0455
   - 4.95% = 0.0495
   - 7.95% = 0.0795

2. Use the formula for the geometric mean of these growth rates:

\[
\text{CAGR} = \left( (1 + g_1) \times (1 + g_2) \times (1 + g_3) \times (1 + g_4) \times (1 + g_5) \right)^{\frac{1}{n}} - 1
\]

Where:
- \(g_1, g_2, \dots, g_5\) are the growth rates in decimal form.
- \(n = 5\) (the number of periods).

3. Plug in the values and calculate.

\[
\text{CAGR} = \left( (1 + 0.0525) \times (1 + 0.0635) \times (1 + 0.0455) \times (1 + 0.0495) \times (1 + 0.0795) \right)^{\frac{1}{5}} - 1
\]

Let me compute this for you.The compound growth rate (CAGR) based on the given annual growth rates is approximately **5.8%**.

Would you like further details on the process or any related questions? 

Here are 5 questions to expand on this topic:

1. How does CAGR differ from the average annual growth rate?
2. Can we calculate CAGR over a non-integer number of years?
3. What are the uses of CAGR in financial analysis?
4. How do changes in individual annual growth rates affect the compound growth rate?
5. How can we compare CAGR with simple average growth?

**Tip:** When comparing investment options or growth over time, the compound growth rate provides a better understanding of consistent growth across periods than the average growth rate.

Calculate the compound growth rate given the following annual growth rates: 5.25%, 6.35%, 4.55%, 4.95%, 7.95%.

Learn how to calculate the compound growth rate (CAGR) using the geometric mean formula, given a series of annual growth rates: 5.25%, 6.35%, 4.55%, 4.95%, 7.95%. This step-by-step guide shows the conversion of percentages to decimals and the use of the geometric mean formula to find CAGR. Suitable for high school students (Grades 10-12).

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