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?

Group of answer choices

$185,743

$152,374

$127,500

$175,000

Answer 1

To find the value of the house in 2030, we can use the formula for compound interest, which is:

\[
V = P(1 + r)^t
\]

Where:
- \( V \) is the future value of the investment/loan, including interest.
- \( P \) is the principal investment amount (the initial deposit or loan amount).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.

Given:
- \( P = 125,000 \) (the initial price of the house)
- \( r = 0.02 \) (the annual increase of 2%)
- \( t = 2030 - 2010 = 20 \) years

Now, plugging the values into the formula:

\[
V = 125,000(1 + 0.02)^{20}
\]

Calculating \( (1 + 0.02)^{20} \):

\[
(1 + 0.02)^{20} = (1.02)^{20} \approx 1.485947
\]

Now, substituting back into the equation:

\[
V = 125,000 \times 1.485947 \approx 185743.375
\]

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

\[
V \approx 185743
\]

Thus, the value of the house in 2030 is **$185,743**.