Question

David buys a home for $278,640. his home is predicted to increase in value 4% each year. what is the predicted value of david's home in 18 years? round your answer to the nearest dollar.

a. $542,638
b. $564,474
c. $576,284
d. $580,122

Answer 1

The predicted value of David's home in 18 years with a 4% annual increase is calculated using the compound interest formula. After performing the calculation, the predicted value comes to approximately $564,474, which is option (b).

Step-by-step explanation:

The predicted value of David's home in 18 years, given it increases in value by 4% each year, can be calculated using the formula for compound interest: Final Value = Initial Value × (1 + Rate)^Time. In this case, the Initial Value is $278,640, the Rate is 4% or 0.04, and Time is 18 years.

Using the formula, we get:

• Final Value = $278,640 × (1 + 0.04)^18

Calculating this we find:

• Final Value = $278,640 × (1.04)^18
• Final Value = $278,640 × 2.02522...
• Final Value ≈ $564,474 (rounded to the nearest dollar)

Therefore, the predicted value of David's home in 18 years is approximately $564,474, which corresponds to option (b).