To calculate the future value of Fred's house in 2030, we can use the formula for compound interest:
\[ FV = PV \times (1 + r)^n \]
where:
- \( FV \) is the future value,
- \( PV \) is the present value (initial amount),
- \( r \) is the annual interest rate (as a decimal), and
- \( n \) is the number of years.
In this case:
- \( PV = 250,000 \),
- \( r = 0.08 \) (8% expressed as a decimal), and
- \( n = 2030 - 2020 = 10 \).
Now, we can plug the values into the formula:
\[ FV = 250,000 \times (1 + 0.08)^{10} \]
Calculating \( (1 + 0.08)^{10} \):
\[ (1 + 0.08)^{10} = (1.08)^{10} \approx 2.158925 \]
Now, calculating \( FV \):
\[ FV \approx 250,000 \times 2.158925 \approx 539,731.25 \]
Therefore, Fred's house would be worth approximately $539,731.25 in 2030.
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