A house in a subdivision recently sold for $178,000. Sales records show that houses in this neighborhood have appreciated 11% per year for each of the past 3 years. Based on this, what was the estimated value of the house on a straight-line basis, at the end of 3 years?

Rationale

$220,720 is the estimated value of the house at the end of 3 years.

To calculate the future value of the house, we apply the formula for compound interest. Starting with an initial value of $178,000 and appreciating at an 11% rate per year for 3 years, we find the estimated value to be $220,720.

A ($192,240) YOUR ANSWER

This choice results from an incorrect understanding of compound interest. If we simply added 11% once to the original price, it would yield $197,580, but this does not account for the compound growth over three years, leading to a significant underestimation of the house's value.

B ($200,400) YOUR ANSWER

This option appears to be a further miscalculation based on linear appreciation. It seems to reflect an incorrect application of a single year's appreciation, which does not consider the compounding effect of the annual appreciation over three years. The actual growth is much higher due to this compounding nature of the appreciation.

C ($220,720) CORRECT

By correctly using the compound interest formula, the calculation is $ 178,000 \times (1 + 0.11)^3 $, which equals approximately $220,720. This reflects the true appreciation of the property over the 3-year period, accounting for the compounding effect of the 11% annual increase.

D ($224,229) YOUR ANSWER

This choice overestimates the house's value, possibly due to an error in calculating the compound interest. It does not accurately apply the formula for compounding, leading to an inflated figure that exceeds the actual growth based on the given appreciation rate.

Conclusion

The estimated value of the house after 3 years of 11% annual appreciation is accurately calculated to be $220,720. This result highlights the importance of understanding compound interest, as it significantly impacts the growth of investments over time, especially in real estate. Understanding these financial principles allows homeowners and investors to make informed decisions regarding property values.

A house in a subdivision recently sold for $178,000. Sales records show that houses in this neighborhood have appreciated 11% per year for each of the past 3 years. Based on this, what was the estimated value of the house on a straight-line basis, at the end of 3 years?

$220,720 is the estimated value of the house at the end of 3 years.

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