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 .

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 .

Transcript text: 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 $\$ \square$. (Do not round until the final answer. Then round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Identify the Given Values

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: \( 4 \)

Step 2: Apply the Compound Interest Formula

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: \[ FV = 100,000 \times (1 + 0.08)^4 \]

Step 3: Calculate the Future Value

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

Step 4: Round the Future Value

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

Final Answer

\(\boxed{\$136,048.90}\)

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