Two years ago, a house sold for $100,000. Research shows that in this region, houses have been appreciating in value at the rate of 9% per year. What is the indicated value that should be used to establish a listing price?

Rationale

$118,810 should be used to establish a listing price.

To determine the current value of the house that appreciated at a rate of 9% per year for two years, we apply the formula for compound interest. The calculation shows that the house's value has increased to $118,810.

A ($101,808) YOUR ANSWER

This amount does not account for the full appreciation over the two-year period. It appears to be a miscalculation as it suggests a much lower growth rate than the actual 9% compounded annually.

B ($109,000) YOUR ANSWER

This value reflects only one year of appreciation at 9% from the original price of $100,000, resulting in a value of $109,000. However, it fails to include the additional appreciation that occurs in the second year, leading to an underestimation of the house's current value.

C ($118,000) YOUR ANSWER

While this amount is closer to the correct answer, it does not accurately represent the compounded growth over the two years. This figure seems to suggest a linear increase rather than the correct compounded growth calculation, resulting in an underestimation.

D ($118,810) CORRECT

This is the correct calculation using the formula for compound interest: $100,000 × (1 + 0.09)^2 = $100,000 × 1.1881 = $118,810. This accurately reflects the value of the house after two years of appreciation at 9% per year.

Conclusion

To establish a listing price for the house, the compounded appreciation over two years must be accurately calculated. The final value of $118,810 reflects the growth at the specified rate and is essential for ensuring a competitive and realistic listing in the current market. Understanding compound interest is crucial for making informed real estate decisions, as illustrated in this scenario.

Two years ago, a house sold for $100,000. Research shows that in this region, houses have been appreciating in value at the rate of 9% per year. What is the indicated value that should be used to establish a listing price?

$118,810 should be used to establish a listing price.

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