Question

Fred bought a house for $250,000 in 2020. His real estate agent told him that the house's value increased at an average annual rate of 8%.



Calculate how much Fred's house would be worth in 2030. Round to the nearest cent.

Answer 1

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.