To calculate the compound growth rate (also known as the geometric average growth rate), we use the formula:

$CAGR = \left( \prod_{i=1}^{n} (1 + r_i) \right)^{\frac{1}{n}} - 1$

Where:

• $r_i$ are the individual growth rates for each year (expressed as decimals),
• $n$ is the number of growth rates.

For the growth rates provided:

• 4.50% → 0.045
• 5.60% → 0.056
• 3.80% → 0.038
• 4.20% → 0.042
• 7.20% → 0.072

Step-by-step solution:

1. Convert each percentage to a decimal and add 1: $1.045, 1.056, 1.038, 1.042, 1.072$

2. Multiply these values together: $\text{Product} = 1.045 \times 1.056 \times 1.038 \times 1.042 \times 1.072$

3. Take the 5th root of the product (since there are 5 growth rates) and subtract 1 to find the compound growth rate.

Let me calculate that for you.The compound growth rate is approximately 5.05%.

Would you like any additional details or clarifications? Here are some related questions to explore:

1. How does compound growth differ from simple growth?
2. What impact does a negative growth rate have on compound growth?
3. How would the compound growth rate change if there were more years of growth data?
4. What real-world applications use compound growth calculations?
5. How can we apply the compound growth rate formula to financial investments?

Tip: When dealing with growth rates over time, always remember to use the geometric average for accuracy, especially if the rates vary significantly.