Market analysis measures a total 8% increase over 18 months. For a simple, non-compounded monthly average of that total change, what approximate monthly adjustment rate results?
Correct Answer
D) 0.44% per month
The defined simple average is 8%/18=0.4444% per month, approximately 0.44%. A compound monthly rate would instead use 1.08^(1/18)−1. Neither monthly conversion nor this linear time form is mandatory for every market analysis; the appropriate period, price base, dates and method must be supported.
Why This Is the Correct Answer
Option D is correct because a simple, noncompounded monthly average divides the total change by the number of months: 8% / 18 = 0.444% per month, or about 0.44%. A compound monthly rate would use a different formula. The method and period chosen in practice must be supported by the market data.
Why the Other Options Are Wrong
Option A: 2.25% per month
Option A, 2.25% per month, comes from inverting the division: 18 / 8 = 2.25. The total change goes on top and the months underneath, so the correct simple rate is 8% / 18 = 0.44% per month; 2.25% per month would add up to about 40.5% over 18 months, not 8%.
Option B: 0.67% per month
Option B, 0.67% per month, results from dividing 8% by 12 months, as if the change occurred over one year. The change occurred over 18 months, so the correct simple rate is 8% / 18 = 0.44%.
Option C: 8.0% per month
Option C, 8.0% per month, treats the 18-month total as if it were a monthly rate. That would imply a 144% simple change over the period; the correct rate is 8% / 18 = 0.44%.
Total over time
Simple monthly rate equals total percent change divided by the number of months in the period.
How to use: Use this formula to check that the monthly rate times the months returns the original total.
Exam Tip
Multiply your answer back by the number of months; only the correct simple rate will reproduce the stated total change.
Common Mistakes to Avoid
- -Dividing the number of months by the percent change instead of the reverse
- -Dividing by 12 when the period is not one year
- -Treating a total change as if it were a monthly rate
Concept Deep Dive
Analysis
This question tests converting a total market change over a period into a simple monthly rate. A simple average spreads the total change evenly across the months: 8% divided by 18 months. The distractors invert the ratio, divide by the wrong number of periods, or treat the total as monthly.
Background Knowledge
Market conditions adjustments are often expressed as a rate per month or per year so they can be applied to sales of different ages. A simple rate assumes a straight-line change, while a compound rate assumes growth on growth. Either form must match the supported market behavior and the price base used.
Real-World Application
An appraiser's resale analysis shows townhouse prices in a development rose about 8% over the past 18 months. To adjust comparables sold at various dates, the appraiser converts this to roughly 0.44% per month on a simple basis. A sale 6 months old is then adjusted about 2.7% upward.
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