A cash-equivalent resale pair with all other relevant factors controlled moves from $280,000 to $294,000 in exactly 12 months. What annual percentage increase on the original price does this pair indicate?
Correct Answer
C) 5.0%
(294000−280000)÷280000×100=5. Common errors: dividing by the resale price instead of the original price gives 4.8%; reporting the price relative instead of the change gives 105.0%; reporting a monthly rate instead of an annual rate gives 0.4%.
Why This Is the Correct Answer
Option C is correct because the price change is $294,000 − $280,000 = $14,000, and $14,000 ÷ $280,000 × 100 = 5.0%. Since the period is exactly 12 months, this is the annual rate on the original price. Resales of the same property with other factors controlled are a recognized way to measure market conditions change.
Why the Other Options Are Wrong
Option A: 0.4%
Option A, 0.4%, is a monthly rate: 5.0% ÷ 12 ≈ 0.4%. The question asks for the annual increase, and the pair already covers exactly one year, so the answer is 5.0%.
Option B: 4.8%
Option B, 4.8%, divides the change by the resale price instead of the original price: $14,000 ÷ $294,000 × 100 ≈ 4.8%. The rate on the original price is $14,000 ÷ $280,000 = 5.0%.
Option D: 105.0%
Option D, 105.0%, is the price relative, $294,000 ÷ $280,000 × 100, not the change. Subtracting 100% from the relative gives the 5.0% increase.
Change over the start
Percent change equals (new minus old) divided by old; the starting price is the base.
How to use: Use this whenever you compute a growth rate from a sale and resale.
Exam Tip
Look for the base the question names, here the original price. A figure above 100% usually signals that a ratio was reported instead of a change.
Common Mistakes to Avoid
- -Dividing the price change by the later sale price
- -Reporting the ratio of the two prices instead of the change
- -Converting to a monthly rate when an annual rate is asked
Concept Deep Dive
Analysis
This question tests how to extract an annual rate of change from a controlled resale pair. Because the pair spans exactly 12 months and other factors are controlled, the percentage change on the original price is the annual rate. The key is dividing the dollar change by the original (earlier) price, not the later price.
Background Knowledge
A matched resale of the same property, with no significant change in the property between sales, can indicate the market conditions change over the period. A simple rate is measured against the original price. Time adjustments must be supported by evidence such as this.
Real-World Application
An appraiser finds a house that sold twice, a year apart, with no renovations between sales. The appraiser uses the resale pair, along with other market data, to support a market conditions adjustment for older comparables.
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