Question

A family bought a house for $125,000 in 2010. The value of the house increased by 2% each year.

What would the value of the house be in 2030, to the nearest dollar?

Answer 1

To calculate the future value of the house in 2030, we can use the formula for compound interest:

\[
\text{Future Value} = P(1 + r)^n
\]

where:
- \( P \) is the principal amount (the initial value of the house),
- \( r \) is the annual growth rate (as a decimal),
- \( n \) is the number of years.

In this case:
- \( P = 125,000 \)
- \( r = 0.02 \) (which is 2% expressed as a decimal)
- The number of years from 2010 to 2030 is \( n = 20 \).

Now substitute the values into the formula:

\[
\text{Future Value} = 125,000 \times (1 + 0.02)^{20}
\]

First, calculate \( (1 + 0.02)^{20} \):

\[
(1 + 0.02)^{20} = (1.02)^{20}
\]

Calculating \( (1.02)^{20} \):

\[
(1.02)^{20} \approx 1.488864
\]

Now, multiply by the initial value:

\[
\text{Future Value} \approx 125,000 \times 1.488864 \approx 186,105.50
\]

Rounding to the nearest dollar, the value of the house in 2030 would be:

\[
\text{Future Value} \approx 186,106
\]

So, the value of the house in 2030 is **$186,106**.