A house with no physical changes sold for $300,000 and resold for $318,000 fourteen months later. Using simple annualization with no compounding, what annualized percentage change is indicated, rounded to one decimal place?
Correct Answer
B) 5.1 percent per year
Total change = ($318,000 − $300,000)/$300,000 = 6%; simple annualized rate = 6% × 12/14 = 5.1429%, rounded to 5.1%. Keep the stated numerator, denominator and units distinct. Common errors: reporting the total change without annualizing gives 6.0 percent per year; reporting a monthly rate instead of an annual rate gives 0.4 percent per year; multiplying by 14/12 instead of 12/14 gives 7.0 percent per year.
Why This Is the Correct Answer
Option B is correct because the total change is ($318,000 - $300,000) / $300,000 = 6%, and simple annualization gives 6% x 12 / 14 = 5.1429%, which rounds to 5.1 percent per year. Because the holding period was longer than a year, the annual rate must be lower than the total change.
Why the Other Options Are Wrong
Option A: 0.4 percent per year
Option A, 0.4 percent per year, is actually a monthly rate: 6% / 14 = 0.43%, which rounds to 0.4. The annual rate is 6% x 12 / 14 = 5.1%.
Option C: 6.0 percent per year
Option C, 6.0 percent per year, is the total change over 14 months, ($318,000 - $300,000) / $300,000 = 6%, reported without annualizing. Scaling to 12 months gives 6% x 12 / 14 = 5.1%.
Option D: 7.0 percent per year
Option D, 7.0 percent per year, comes from multiplying by 14/12 instead of 12/14: 6% x 14 / 12 = 7.0%. The correct factor is 12/14, giving 5.1%.
Longer than a year, shrink it
If the change took more than 12 months, the annual rate is smaller than the total change; if less than 12 months, it is larger.
How to use: Use this check to confirm you multiplied by 12 over the months held, not the reverse.
Exam Tip
After annualizing, compare with the total change: a 14-month period should give an annual rate below the 6% total.
Common Mistakes to Avoid
- -Reporting the total change as the annual rate
- -Inverting the time factor to 14/12
- -Using a resale of a property that was renovated between sales
Concept Deep Dive
Analysis
This question tests a paired-resale market-conditions calculation with simple annualization. First find the total percentage change over 14 months, then scale it to 12 months by multiplying by 12/14. Distractors come from skipping annualization, using a monthly rate or inverting the time ratio.
Background Knowledge
Measuring the difference in sale prices when the same unchanged property sells more than once over time is a recognized way to support a market-conditions (time) adjustment. Simple annualization prorates the total change by time, while compounding would treat each period's gain as building on the last.
Real-World Application
An appraiser finds an unchanged house that resold for $318,000 fourteen months after selling for $300,000. She uses the paired resale, along with other market evidence, to support a time adjustment of roughly 5% per year.
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