Questions: What will a 100,000 house cost 4 years from now if the price appreciation for homes over that period averages 8% compounded annually? The future cost of the house will be .

Solution Steps

We are given the following values:

• Current value of the house: $\$100,000$
• Annual appreciation rate: $8\%$ or $0.08$ as a decimal
• Number of years: $4$

To find the future value of the house, we use the compound interest formula: $$FV = PV \times (1 + r)^n$$ where:

• $FV$ is the future value of the house,
• $PV$ is the present value (\$100,000),
• $r$ is the annual appreciation rate (0.08),
• $n$ is the number of years (4).

Substituting the given values: $$FV = 100,000 \times (1 + 0.08)^4$$

Calculate the future value using the formula: $$FV = 100,000 \times (1.08)^4$$ $$FV = 100,000 \times 1.3605$$ $$FV = 136,048.896$$

Round the future value to the nearest cent: $$FV \approx 136,048.90$$

Final Answer