Closed sales in a market area were 50 in the prior period and 55 in the current period, and the two periods are the same length. What is the percent change in closed sales?
Correct Answer
C) 10 percent
The count rose by 55 − 50 = 5 sales. Relative change = 5/50 = 0.10, or 10%. Current/prior ×100 gives 110% of the original level, not the percentage increase. Comparable period lengths and definitions are necessary for interpretation. 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 closed sales rose by 55 − 50 = 5 sales. Dividing that change by the prior-period figure gives 5/50 = 0.10, and multiplying by 100 gives 10 percent. Comparable period lengths and definitions make the comparison meaningful.
Why the Other Options Are Wrong
Option A: 1 percent
Option A, 1 percent, misplaces the decimal by multiplying by 10 instead of 100: (55 − 50)/50 × 10 = 1. The correct calculation is 5/50 × 100 = 10 percent.
Option B: 9 percent
Option B, 9 percent, divides by the current figure instead of the prior figure: (55 − 50)/55 × 100 = about 9 percent. Percent change uses the starting value as the base, so 5/50 × 100 = 10 percent.
Option D: 110 percent
Option D, 110 percent, reports the current level as a percentage of the prior level: 55/50 × 100 = 110 percent. That shows current sales are 110 percent of the original level, but the increase is 10 percent.
New minus old, over old
Percent change equals new minus old, divided by old, times 100. The old value is the base.
How to use: Use this phrase to set up any period-over-period percent change.
Exam Tip
Check which number is the starting value and divide by it. A result above 100 percent for a small change usually means you computed a level, not a change.
Common Mistakes to Avoid
- -Dividing the change by the current figure instead of the prior figure
- -Reporting the ratio of current to prior as the percent change
- -Multiplying by 10 instead of 100
Concept Deep Dive
Analysis
This question tests the percent-change formula. Percent change is the difference between the new and old figures divided by the old figure, times 100. Here (55 − 50)/50 × 100 = 10 percent; the key is to divide by the prior period, not the current one.
Background Knowledge
Percent change measures how much a figure moved relative to its starting point. Appraisers use period-over-period changes in closed sales, prices and listings as market-conditions evidence. Comparisons are meaningful only when the periods have similar lengths and the data use the same definitions.
Real-World Application
An appraiser completing a market conditions analysis sees closed sales go from 50 in the prior period to 55 in the current period. The appraiser reports a 10 percent increase in closed sales. The appraiser also confirms the periods cover the same number of months.
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