Two sales are alike except for a fireplace and their sale dates. The home with a fireplace sold for $265,000 six months before the effective date, and the home without a fireplace sold for $258,000 at the effective date. Market values rose at a simple rate of 0.5% per month during that time. After adjusting the older sale for market conditions, what contribution does the pair indicate for the fireplace?
Correct Answer
C) $14,950
265000 × (1 + 0.005 × 6) − 258000 = 14950. Common errors: not time-normalizing the older sale gives $7,000; adjusting the older sale downward instead of upward gives −$950; misplacing the decimal in the 0.5% rate gives $86,500.
Why This Is the Correct Answer
Option C is correct because $265,000 × (1 + 0.005 × 6) = $265,000 × 1.03 = $272,950, and $272,950 − $258,000 = $14,950. Once both sales are in effective-date dollars, the only remaining difference is the fireplace. That difference is the contribution the time-normalized pair indicates.
Why the Other Options Are Wrong
Option A: −$950
Option A, −$950, results from adjusting the older sale downward instead of upward: $265,000 × (1 − 0.005 × 6) − $258,000 = $257,050 − $258,000 = −$950. The market change is an increase, so the correct figure is $272,950 − $258,000 = $14,950.
Option B: $7,000
Option B, $7,000, is the raw difference $265,000 − $258,000, which skips time-normalizing the older sale. The six-month market change must be removed first, giving $272,950 − $258,000 = $14,950.
Option D: $86,500
Option D, $86,500, comes from misplacing the decimal in the 0.5% rate: $265,000 × (1 + 0.05 × 6) − $258,000 = $344,500 − $258,000 = $86,500. Using 0.005 per month gives the correct $14,950.
Same date, then compare
A pair can only isolate a feature when all other factors, including the date, are the same. Normalize the date first, then subtract.
How to use: Use this check whenever a paired sales question gives two different sale dates.
Exam Tip
When a paired sales question mentions a time change, the raw price difference is usually a distractor. Convert 0.5% to 0.005 before multiplying.
Common Mistakes to Avoid
- -Using the raw price difference without adjusting for the sale dates
- -Adjusting the older sale downward in a rising market
- -Writing 0.5% as 0.05 instead of 0.005
Concept Deep Dive
Analysis
This question tests paired sales analysis when the two sales are from different dates. Before the price difference can be credited to the fireplace, the older sale must be brought to the effective date. Adjust the $265,000 sale upward by 0.5% × 6 = 3%, then subtract the $258,000 sale to isolate the fireplace contribution.
Background Knowledge
Paired sales analysis isolates the price effect of one feature by comparing sales that differ only in that feature. When the sales occurred at different times, a supported market-conditions adjustment must first put them on the same date basis. Fannie Mae recognizes paired sales as one way to determine adjustment rates.
Real-World Application
An appraiser finds two otherwise matched tract homes, one with a fireplace that sold six months earlier. After applying the market's supported monthly appreciation to the older sale, the appraiser uses the remaining difference as evidence of the fireplace's contribution.
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