# 8 1 practice geometric mean

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## The Importance of Geometric Mean in Financial Calculations

As a website operator, it’s important to understand the basics of financial calculations in order to provide accurate and useful information to your visitors. One key tool in financial calculations is the geometric mean, which is used to determine the average rate of return on an investment or portfolio over a specific period of time.

Unlike the arithmetic mean, which simply calculates the average of a set of numbers, the geometric mean takes into account the compounding of returns over time. This makes it a more accurate representation of investment performance, especially for long-term investments.

## Example Calculation

Let’s say that an investment starts with \$10,000 and earns a 5% return in the first year, a 10% return in the second year, and a 15% return in the third year. To calculate the geometric mean, we would first calculate the product of the three returns:

(1.05) x (1.10) x (1.15) = 1.357875

Next, we would take the cube root of this product to calculate the geometric mean:

(1.357875)^(1/3) = 1.120656

This means that the investment had an average annual rate of return of 12.07% over the three-year period.

## Using Geometric Mean in Financial Analysis

Geometric mean is an important tool for investors because it allows them to accurately compare the performance of different investments over time. For example, if an investor is considering two mutual funds, one that has returned 8% annually for the past five years and another that has returned 10% annually for the past three years, they can use the geometric mean to compare the two investments on an equal basis.