Market data for one market area show a prior-year median closed sale price of $400,000 and a current-year median closed sale price of $440,000. What is the year-over-year percent change in the median sale price?
Correct Answer
C) 10 percent
Percentage change = (440000 − 400000)/400000 × 100 = 10%. Keep the stated numerator, denominator and units distinct. Common errors: dividing by the current figure instead of the prior figure gives 9 percent; reporting the current level as a percentage of the prior level gives 110 percent; misplacing the decimal (×10 instead of ×100) gives 1 percent.
Why This Is the Correct Answer
Option C is correct because the percent change is (440,000 - 400,000) / 400,000 x 100 = 10%. The prior-year median is the base, so the $40,000 increase is 10% of it.
Why the Other Options Are Wrong
Option A: 1 percent
Option A, 1 percent, comes from misplacing the decimal: (440,000 - 400,000) / 400,000 x 10 = 1. Multiplying by 100 gives the correct 10%.
Option B: 9 percent
Option B, 9 percent, comes from dividing by the current figure instead of the prior figure: 40,000 / 440,000 x 100 = 9.09, about 9. Percent change uses the earlier value as the base, giving 10%.
Option D: 110 percent
Option D, 110 percent, reports the current level as a percentage of the prior level: 440,000 / 400,000 x 100 = 110. That is a ratio, not a change; subtracting 100 gives the 10% increase.
New minus old, over old
Percent change equals new minus old, divided by old, times 100.
How to use: Use this phrase for any percent-change question to keep the base value correct.
Exam Tip
If an answer is about 100 higher than another plausible answer, it is likely a ratio rather than a change.
Common Mistakes to Avoid
- -Dividing by the newer figure instead of the older one
- -Reporting the ratio of new to old as the percent change
- -Multiplying by 10 instead of 100
Concept Deep Dive
Analysis
This question tests a basic percent change calculation. Subtract the prior figure from the current figure, divide by the prior figure, and multiply by 100. Distractors come from using the wrong base, reporting a ratio instead of a change, and misplacing the decimal.
Background Knowledge
Year-over-year changes in median sale price are a common indicator of market trend in residential appraisal. Percent change measures the difference relative to the starting value. Appraisers should also consider whether the mix of properties sold changed, since a median can shift for reasons other than price movement.
Real-World Application
An appraiser compares the median closed price of competing homes this year with last year to report the trend on a market conditions form. She notes the 10% rise but also checks whether larger homes made up more of this year's sales.
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