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

$127,500

$152,374

$185,743

$175,000

Answer 1

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

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

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),
- \( n \) is the number of years the money is invested or borrowed.

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

Now, substituting in the values:

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

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

\[
(1.02)^{20} \approx 1.485947
\]

Now we substitute this back into the formula:

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

To the nearest dollar, the value of the house in 2030 would be approximately **$185,743**.

So the correct answer is:

**$185,743**