46. A house in a subdivision recently sold for $178,000. Sales records show that houses in this neighborhood have appreciated 8% per year for each of the past 3 years. If the economic trend continues at this rate, the house will be worth how much, on a compound basis, at the end of 3 years?
Answer: D
The house will be worth $224,229 at the end of 3 years.
To determine the future value of the house after 3 years of appreciation at a rate of 8% per year, we apply the formula for compound interest. Using the initial value of $178,000, the future value can be calculated as $178,000 * (1 + 0.08)^3, which results in $224,229.
A) $192,240
This option is incorrect as it does not account for the compound nature of the appreciation. Instead, it appears to assume a simple interest calculation or an incorrect application of the percentage increase over three years.
B) $206,480
Option B miscalculates the compounded growth as well. This figure may represent a partial or incorrect application of the appreciation rate, but it does not reflect the correct compounded value after three years.
C) $220,720
While this option is closer to the correct amount, it still fails to accurately apply the compounded interest formula. This figure likely results from an error in calculating the total appreciation over the three-year period, not incorporating the compounding effect properly.
D) $224,229
This option accurately reflects the future value of the house after applying the compound interest formula correctly. The calculation of $178,000 * (1 + 0.08)^3 yields the exact total, confirming this as the correct answer.
Conclusion
The correct answer of $224,229 is derived from properly applying the compound interest formula, reflecting the annual appreciation of the property over three years. All other options fail to account for the compounding effect, resulting in lower or incorrect valuations. Thus, option D stands as the definitive solution.