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

$224,229

To find the future value of the house after 3 years of appreciation at a rate of 8% per year, we use the formula for compound interest: $ FV = P(1 + r)^n $, where $ P $ is the principal amount, $ r $ is the interest rate, and $ n $ is the number of years. Substituting the values gives us $ FV = 178,000(1 + 0.08)^3 = 178,000 \times 1.259712 = 224,229 $.

A ($192,240) YOUR ANSWER

This amount represents an incorrect calculation of the future value. It seems to reflect a simple interest calculation rather than compound interest, which does not account for the annual appreciation compounding over the three years.

B ($206,480) YOUR ANSWER

This figure also fails to apply the compound interest formula correctly. It might represent the value after two years of appreciation at 8%, which does not consider the full three-year compounding effect needed for an accurate future value.

C ($220,720) YOUR ANSWER

While this option is closer to the correct answer, it is still an incorrect calculation. It likely results from miscalculating the compounding effect, as it does not fully incorporate the compounding growth over the three years as required by the compound interest formula.

D ($224,229) CORRECT

This is the correct future value of the house after 3 years of appreciating at an 8% annual rate, accurately calculated using the compound interest formula.

Conclusion

The future value of the house after 3 years of 8% annual appreciation is correctly determined to be $224,229. This value illustrates the impact of compound interest over time, showing how the initial investment grows significantly when appreciation compounds annually rather than applying a simple interest approach. Each incorrect option reflects misunderstandings of the compound interest calculation, emphasizing the importance of using the correct formula for accurate financial forecasting.

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?

$224,229

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