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 1.1311.131, 1.0431.043, and 1.0211.021 is approximately 1.0641.064, rounded to four decimal places.

Would you like further details or have any questions?

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.

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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