The geometric mean is often used in business and economics for finding average rates of​ change, average rates of​ growth, or average ratios. Given n values​ (all of which are​ positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 13.1​%, 4.3​%, and 2.1​% can be found by computing the geometric mean of 1.131​, 1.043​, and 1.021. Find that average growth​ factor, or geometric mean. (Round to four decimal places as needed.)

The average growth factor, or geometric mean, of the given values \(1.131\), \(1.043\), and \(1.021\) is approximately \(1.064\), rounded to four decimal places.

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Here are five related questions you might find helpful:
1. What is the difference between the arithmetic mean and geometric mean?
2. How do interest rates compound in a financial context?
3. Can the geometric mean be used for negative values?
4. How does geometric mean apply in measuring stock market returns?
5. Why is the geometric mean more appropriate for growth rates than the arithmetic mean?

**Tip:** The geometric mean is often preferred in finance because it reflects the compounding effect over time, especially when dealing with growth rates.

The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values​ (all of which are​ positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 13.1​%, 4.3​%, and 2.1​% can be found by computing the geometric mean of 1.131​, 1.043​, and 1.021. Find that average growth​ factor, or geometric mean. (Round to four decimal places as needed.)

Learn how to calculate the geometric mean for growth rates with annual interest rates of 13.1%, 4.3%, and 2.1%. Understand the application of geometric means in business and economics for finding average rates of change and growth. Suitable for students in Grades 10-12 or early college level.

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