Tom’s house cost $160,000 in the year 2000. In 2008 he sold his house for $208,000.



Tom's house increased in value from $160,000 in 2000 to $208,000 in 2008. To analyze this change, we can calculate the following:

### 1. **Absolute Increase in Value**
The absolute increase in the house's value is:
\[
\text{Increase} = 208,000 - 160,000 = 48,000
\]
So, the house's value increased by $48,000.

### 2. **Percentage Increase in Value**
We can calculate the percentage increase using the formula:
\[
\text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original Value}} \right) \times 100
\]
Substitute the values:
\[
\text{Percentage Increase} = \left( \frac{48,000}{160,000} \right) \times 100 = 30\%
\]
So, the house increased in value by **30%** over 8 years.

### 3. **Annual Growth Rate (Compound Growth)**
To calculate the annual compound growth rate, we use the formula:
\[
\text{Growth Rate} = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1
\]
where $n$ is the number of years.

Substitute the values:
\[
\text{Growth Rate} = \left( \frac{208,000}{160,000} \right)^{\frac{1}{8}} - 1 \approx 0.0342
\]
Multiply by 100 to convert to a percentage:
\[
\text{Growth Rate} \approx 3.42\%
\]
So, the annual compound growth rate was approximately **3.42%** per year.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the results change if the house had sold for $250,000?
2. What if Tom bought the house with a mortgage and had to pay interest?
3. How does compound interest compare with simple interest in this scenario?
4. How long would it take for the house to double in value at this growth rate?
5. How does the house's appreciation compare to average inflation rates?

**Tip:** When calculating percentage increase, always subtract the initial value from the final value, then divide by the initial value!

Tom’s house cost $160,000 in the year 2000. In 2008 he sold his house for $208,000.

This problem analyzes the increase in house value from $160,000 in 2000 to $208,000 in 2008. Learn how to calculate the absolute increase, percentage increase, and annual compound growth rate with detailed formulas and steps. Suitable for students in Grades 9-12.

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