Raj purchases a new home for $100,000. The value of the home increases by 8% every 3 years. Determine the value of the home after 5 years.

After 5 years, the home is worth $?. Round your answer to the nearest cent.

To calculate the value of the home after 5 years with an 8% increase every 3 years, we can use the formula for exponential growth:

\[
\text{Future Value} = \text{Present Value} \times \left( 1 + \frac{\text{Rate}}{100} \right)^{\frac{\text{Time}}{\text{Period}}}
\]

Where:
- Present Value = $100,000
- Rate = 8% (increase every 3 years)
- Time = 5 years
- Period = 3 years (since the rate applies every 3 years)

### Step 1: Apply the formula

\[
\text{Future Value} = 100,000 \times \left( 1 + \frac{8}{100} \right)^{\frac{5}{3}}
\]
\[
\text{Future Value} = 100,000 \times \left( 1.08 \right)^{\frac{5}{3}}
\]

### Step 2: Calculate the exponent

First, compute the exponent $ \frac{5}{3} \approx 1.6667 $.

\[
1.08^{1.6667} \approx 1.1318
\]

### Step 3: Multiply to get the future value

\[
\text{Future Value} = 100,000 \times 1.1318 = 113,180
\]

So, after 5 years, the home is worth **$113,180.00**.

Would you like to explore other related concepts or have any further questions?

### Related Questions:
1. What would the value of the home be after 10 years with the same growth rate?
2. How does compound interest differ from this exponential growth model?
3. How do you calculate the annual percentage increase in this scenario?
4. What if the value increased by a different percentage every 3 years? How would that affect the calculations?
5. How can you estimate the time needed for the home value to double?

### Tip:
When dealing with percentage growth over time, always remember to adjust the time period to match how often the rate applies, as in this case, every 3 years.

Raj purchases a new home for $100,000. The value of the home increases by 8% every 3 years. Determine the value of the home after 5 years.

Learn how to calculate the future value of a home purchased for $100,000 with an 8% growth rate every 3 years. This detailed example explains exponential growth and percentage increase, providing a solution for determining the value after 5 years. Suitable for students in Grades 9-12.

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