A property sold for $300,000 and resold for $336,000 after 24 months. Both sales were verified and cash equivalent, nothing about the property or transaction changed between them, and other influences are controlled. What is the indicated monthly percentage change, as a simple rate on the original price?
Correct Answer
C) 0.50%
(336000−300000)÷300000÷24×100=0.5. Common errors: dividing by the resale price instead of the original price gives 0.45%; reporting the total change without dividing by the 24 months gives 12.00%; computing a compound rate when a simple rate is asked for gives 0.47%.
Why This Is the Correct Answer
Option C is correct because ($336,000 − $300,000) ÷ $300,000 = 12%, and 12% ÷ 24 months = 0.50% per month. The simple rate is based on the original price, as the question asks. The pair is controlled, so the whole change is attributed to market conditions.
Why the Other Options Are Wrong
Option A: 0.45%
Option A, 0.45%, comes from dividing by the resale price instead of the original price: $36,000 ÷ $336,000 ÷ 24 × 100 = 0.45%. The correct base is the original $300,000, giving $36,000 ÷ $300,000 ÷ 24 × 100 = 0.50%.
Option B: 0.47%
Option B, 0.47%, comes from computing a compound rate when a simple rate is asked for: ((336,000 ÷ 300,000)^(1/24) − 1) × 100 = 0.47%. The simple rate is 12% ÷ 24 = 0.50%.
Option D: 12.00%
Option D, 12.00%, comes from reporting the total change without dividing by the 24 months: $36,000 ÷ $300,000 × 100 = 12.00%. The monthly rate is 12% ÷ 24 = 0.50%.
Change, base, months
Divide the change by the original price, then by the months.
How to use: Use this to extract a simple monthly rate from a resale pair.
Exam Tip
Read whether the question asks for a simple or compound rate, and use the original price as the base for a simple rate.
Common Mistakes to Avoid
- -Dividing by the resale price instead of the original price
- -Forgetting to divide the total change by the months
- -Using a compound rate when a simple rate is specified
Concept Deep Dive
Analysis
This question tests extracting a simple monthly rate from a resale pair. Find the total change, divide by the original price, and then divide by the number of months. The question asks for a simple rate on the original price, not a compound rate.
Background Knowledge
Resales of the same property over time can measure market conditions when nothing else about the property or transaction changed. A simple rate spreads the total percentage change evenly over the months, based on the original price. Compound rates build on prior growth and give a slightly lower monthly figure.
Real-World Application
A house sold for $300,000 and resold unchanged two years later for $336,000. The appraiser derives about 0.5% per month and compares it with other market evidence before applying a time adjustment.
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