Math Problem Statement
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.)
Solution
The average growth factor, or geometric mean, of the given values , , and is approximately , rounded to four decimal places.
Would you like further details or have any questions?
Here are five related questions you might find helpful:
- What is the difference between the arithmetic mean and geometric mean?
- How do interest rates compound in a financial context?
- Can the geometric mean be used for negative values?
- How does geometric mean apply in measuring stock market returns?
- 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.
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Math Problem Analysis
Mathematical Concepts
Geometric Mean
Growth Rate
Business Mathematics
Formulas
Geometric Mean = (x1 * x2 * ... * xn)^(1/n)
Theorems
Properties of Geometric Mean
Suitable Grade Level
Grades 10-12 or early college level
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