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

Rationale

The house will be worth $224,229 at the end of 3 years.

To calculate the future value of the house after appreciating at a rate of 8% per year for 3 years, we use the formula for compound interest: $FV = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. Plugging in the values, we compute $178,000(1 + 0.08)^3$, which results in approximately $224,229.

A (192,240) YOUR ANSWER

This value results from applying a simple interest calculation rather than compound interest. It represents an incorrect assumption of the appreciation being linear rather than exponential, leading to a significant underestimation of the house's future value.

B (206,480) YOUR ANSWER

This option seems to reflect an incomplete calculation of compound interest. It likely arises from misapplying the formula or failing to correctly account for the effect of compounding over three years, resulting in a figure that is still lower than the correct future value.

C (220,720) YOUR ANSWER

While this figure is closer to the correct answer, it still does not account for the full effect of compounding over three years. It suggests a misunderstanding of the compounding process, which should yield a higher future value than calculated here.

D (224,229) CORRECT

This is the correct calculation for the future value of the house after three years, reflecting the compound interest accurately. It utilizes the full compounding effect of the annual appreciation rate applied across the three years.

Conclusion

The calculation of future value using compound interest is crucial in understanding how investments appreciate over time. In this scenario, applying the correct formula reveals that the house will worth $224,229 after three years of 8% annual appreciation. The other choices demonstrate common miscalculations that overlook the importance of compounding, ultimately leading to lower estimated values.

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

The house will be worth $224,229 at the end of 3 years.

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