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 .
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×(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×(1+0.08)4
Step 3: Calculate the Future Value
Calculate the future value using the formula:
FV=100,000×(1.08)4FV=100,000×1.3605FV=136,048.896
Step 4: Round the Future Value
Round the future value to the nearest cent:
FV≈136,048.90