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Sales ComparisonHARD16.4% of exam

Two verified otherwise-matched sales differ only in one bathroom and six months of market time. Sale A at $302,000 has fewer bathrooms; later Sale B with the extra bathroom is $311,000. Evidence supports a simple prorated 4% annual increase on the earlier price, with other material influences controlled. What bathroom contribution is indicated?

Correct Answer

C) $2,960, after removing the time effect

Six months at the stipulated simple 4% annual rate equals 2% of the earlier $302,000 base. Normalize it to 302000×1.02=$308,040. The remaining 311000−308040=$2,960 is the conditional bathroom indication. The raw $9,000 difference ignores time; adding the $6,040 effect instead gives $15,040. This result depends on the expressly controlled remaining differences.

Answer Options
A
$9,000, the raw difference in prices
B
$15,040, adding the market movement
C
$2,960, after removing the time effect
D
$4,500, splitting the difference evenly

Why This Is the Correct Answer

Option C is correct because six months at 4% per year is 2%, so Sale A normalized to Sale B's date is $302,000 x 1.02 = $308,040. The remaining difference, $311,000 - $308,040 = $2,960, is the indicated bathroom contribution with other influences controlled.

Why the Other Options Are Wrong

Option A: $9,000, the raw difference in prices

Option A, $9,000, is the raw difference ($311,000 - $302,000). It ignores the $6,040 of the difference that came from market movement over the six months.

Option B: $15,040, adding the market movement

Option B, $15,040, adds the $6,040 time effect to the $9,000 raw difference instead of subtracting it. Removing the time effect gives $9,000 - $6,040 = $2,960.

Option D: $4,500, splitting the difference evenly

Option D, $4,500, simply halves the $9,000 raw difference ($9,000 / 2). There is no basis for splitting the difference evenly; the time effect must be calculated: $311,000 - $302,000 x 1.02 = $2,960.

Remove time, then read the pair

Bring the earlier sale forward to the later date first; whatever price gap remains belongs to the feature.

How to use: Use this whenever a paired-sales question includes a time difference.

Exam Tip

Convert the annual rate to the actual holding period before multiplying, and apply it to the price base the stem names.

Common Mistakes to Avoid

  • -Treating the raw price difference as the feature's value
  • -Adding the time effect instead of removing it
  • -Applying the full annual rate to a six-month period

Concept Deep Dive

Analysis

This question tests paired-sales extraction when two sales differ in both a feature and timing. The time effect must be removed before the remaining price difference is attributed to the bathroom. Six months at a simple 4% annual rate is a 2% adjustment on the earlier sale.

Background Knowledge

Paired data analysis isolates the value of one feature by comparing sales that differ only in that feature. When the sales also differ in date, the appraiser first adjusts for market conditions so that the remaining difference reflects the feature being studied.

Real-World Application

An appraiser finds two nearly identical townhouses, one with an extra bathroom that sold six months later in a rising market. After adjusting the earlier sale for the market trend, only a modest difference remains, which the appraiser uses as one indication of the bathroom's contribution.

paired sales analysismarket conditions adjustmentbathroom contributiontime adjustmentextraction
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