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.)
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Solution

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Solution Steps

Step 1: Identify the Given Values

We are given the following values:

  • Current value of the house: $100,000 \$100,000
  • Annual appreciation rate: 8% 8\% or 0.08 0.08 as a decimal
  • Number of years: 4 4
Step 2: Apply the Compound Interest Formula

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

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

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

Step 3: Calculate the Future Value

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

Step 4: Round the Future Value

Round the future value to the nearest cent: FV136,048.90 FV \approx 136,048.90

Final Answer

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

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