in the year 1985, a house was valued at $108,000. by the yrar 2005, the value hade appreciated to $149, 000. What was the annual growth rate between 1985 and 2005?

To find the annual growth rate of the house's value between 1985 and 2005, we can use the formula for compound annual growth rate (CAGR):

\[
CAGR = \left( \frac{V_f}{V_i} \right)^{\frac{1}{t}} - 1
\]

Where:
- $ V_f $ is the final value (in 2005), which is $149,000,
- $ V_i $ is the initial value (in 1985), which is $108,000,
- $ t $ is the time in years, which is $ 2005 - 1985 = 20 $ years.

Substitute the values into the formula:

\[
CAGR = \left( \frac{149,000}{108,000} \right)^{\frac{1}{20}} - 1
\]

Now, let's calculate this.The annual growth rate (CAGR) of the house's value between 1985 and 2005 is approximately **1.62%**.

Would you like more details or have any questions? 

Here are 5 related questions:
1. How does compound annual growth rate (CAGR) differ from average growth rate?
2. If the house continues to grow at the same rate, what will its value be in 2025?
3. Can we calculate the future value of the house after 10 more years using the same growth rate?
4. How does inflation affect the interpretation of this growth rate over time?
5. What would be the total percentage increase in the house's value from 1985 to 2005?

**Tip**: The compound annual growth rate (CAGR) smooths out the effects of volatility over a period, showing the average growth rate per year.

In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to $149,000. What was the annual growth rate between 1985 and 2005?

Find out how to calculate the compound annual growth rate (CAGR) for a house whose value increased from $108,000 in 1985 to $149,000 in 2005. This problem explores the use of the CAGR formula and is suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation