3. 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?
Answer: D
The indicated value that should be used to establish a listing price is $118,810.
To determine the appropriate listing price for the house, we must calculate its appreciated value over the past two years at an annual rate of 9%. This calculation results in an indicated value of $118,810.
A) $101,808
This value represents a minimal increase and does not accurately reflect the appreciation rate over two years. If calculated, $101,808 would imply a much lower rate of appreciation than 9%, making this option incorrect.
B) $109,000
While this value shows some increase, it still falls short of the correct appreciation calculation. It does not account for the compounded growth over the two-year period at the specified rate of 9%, and therefore is not an accurate listing price.
C) $118,000
Although this value is closer to the correct answer, it does not properly account for the full compounded growth over two years at the 9% rate. The calculation that leads to $118,000 neglects the additional appreciation that occurs in the second year, making it an insufficient amount for the listing price.
D) $118,810
This is the correct answer as it accurately reflects the compounded appreciation of the house over two years at a rate of 9% per year. The calculation follows the formula: $100,000 * (1 + 0.09)^2, resulting in an appropriate listing price that reflects current market conditions.
Conclusion
The correct answer, $118,810, accurately incorporates the compounded appreciation rate of 9% applied over the two-year period, making it the most suitable listing price. All other options fail to meet this calculation, either underestimating the appreciation or not accounting for the compounding effect, thus validating the choice of $118,810 as the indicated value.