In the year 1985, a house was valued at  $110,000
 . By the year 2005, the value had appreciated to  $145,000
 . What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?

 

Round your answers to two decimal places.

 

The annual growth rate between 1985 and 2005 is  
Number
%
 .

 

The value of the house in the year 2010 is  
Number
.

 

To solve this problem, we need to find the **annual growth rate** between 1985 and 2005 and then use that rate to determine the value of the house in 2010.

### Step 1: Finding the Annual Growth Rate

The formula for compound annual growth rate (CAGR) is given by:

\[
\text{CAGR} = \left( \frac{V_{\text{final}}}{V_{\text{initial}}} \right)^{\frac{1}{t}} - 1
\]

Where:
- $ V_{\text{final}} $ is the value of the house in 2005 ($145,000),
- $ V_{\text{initial}} $ is the value of the house in 1985 ($110,000),
- $ t $ is the number of years between 1985 and 2005, which is $ t = 2005 - 1985 = 20 $ years.

Now, we plug in the values and solve for the CAGR.

\[
\text{CAGR} = \left( \frac{145,000}{110,000} \right)^{\frac{1}{20}} - 1
\]

### Step 2: Finding the Value of the House in 2010

Once we have the growth rate, we can calculate the house's value in 2010. The formula is:

\[
V_{\text{2010}} = V_{\text{2005}} \times (1 + \text{CAGR})^t
\]

Where:
- $ V_{\text{2005}} = 145,000 $,
- $ t = 2010 - 2005 = 5 $ years.

I'll now compute both steps.The **annual growth rate** between 1985 and 2005 is **1.39%**.

The **value of the house in 2010** is **$155,368.09**.

Would you like more details on the calculations or have any questions?

Here are 5 related questions for further exploration:
1. What would be the value of the house in 2025, assuming the same growth rate?
2. How does compound growth differ from simple growth in such real estate problems?
3. How does the annual growth rate compare if the house value doubled in the same period?
4. What if the house value in 1985 was different? How would the growth rate change?
5. How can inflation be factored into calculating the real growth of the house value?

**Tip:** The compound annual growth rate (CAGR) is a powerful way to describe the average growth over time, smoothing out fluctuations in year-to-year growth.

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?

Learn how to calculate the annual growth rate of a house valued at $110,000 in 1985 that appreciated to $145,000 by 2005. Discover the formula for compound annual growth rate (CAGR) and find out the house's value in 2010, assuming a consistent growth rate. Suitable for students in Grades 9-12.

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