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Sales ComparisonHARD16.4% of exam

A home with a fireplace sold for $420,240. An otherwise identical home without one sold four months earlier for $412,000. The market rose a supported 0.5% per month (simple) over that period. After adjusting for market conditions, what does this pair indicate for the fireplace?

Correct Answer

B) $0

Adjust for market conditions first: $412,000 × (1 + 0.005 × 4) = $420,240. After that adjustment the prices are equal, so the pair indicates no contribution for the fireplace. Paired sales must have occurred at the same time or be adjusted for market conditions.

Answer Options
A
$8,240
B
$0
C
$4,120
D
$16,480

Why This Is the Correct Answer

Option B is correct because the earlier sale adjusted for four months at 0.5% per month is $412,000 × 1.02 = $420,240. That equals the price of the home with the fireplace, so the difference is $420,240 − $420,240 = $0 and the pair indicates no contribution for the fireplace.

Why the Other Options Are Wrong

Option A: $8,240

Option A, $8,240, is the raw difference $420,240 − $412,000, which ignores the market change. Once the earlier sale is adjusted to $420,240 for the 2% rise, the gap disappears.

Option C: $4,120

Option C, $4,120, results from adjusting the earlier sale for only two months (1%) instead of four: $412,000 × 1.01 = $416,120, and $420,240 − $416,120 = $4,120. The full four months at 0.5% is 2%, so the earlier sale becomes $420,240 and the gap is $0.

Option D: $16,480

Option D, $16,480, results from adjusting the earlier sale downward instead of upward: $412,000 × (1 − 0.02) = $403,760, and $420,240 − $403,760 = $16,480. Prices rose over the four months, so the earlier sale is adjusted up to $412,000 × 1.02 = $420,240, leaving a $0 difference.

Time first, then the feature

Adjust paired sales to the same date before reading what the remaining difference says about a feature.

How to use: Use this when a paired sales question gives sales at different dates.

Exam Tip

If a paired sales question mentions a market trend, apply it before subtracting the prices.

Common Mistakes to Avoid

  • -Subtracting raw prices without a time adjustment
  • -Attributing market appreciation to a physical feature
  • -Relying on one pair as conclusive proof

Concept Deep Dive

Analysis

This question tests that paired sales must be adjusted for market conditions before isolating a feature's contribution. Bring the earlier sale forward to the date of the later sale first, then compare. Any remaining difference is the indication for the feature.

Background Knowledge

Paired sales analysis isolates the effect of one difference by comparing otherwise similar sales. The paired sales must have occurred at the same time or be adjusted for market conditions. Otherwise, price changes over time can be mistaken for the value of a feature.

Real-World Application

An appraiser sees that a home with a fireplace sold for about $8,000 more than a similar home without one. After adjusting the earlier sale for four months of market growth, the prices match, so the appraiser does not support a fireplace adjustment from this pair.

paired sales analysismarket conditionscontributory valuefireplacetime adjustment
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