Matched market evidence shows a total 15% price increase over 24 months. Assuming a constant compounded monthly rate, what rate reproduces that total increase? Round the percentage to two decimal places.
Correct Answer
A) 0.58 percent per month
Compound monthly rate = [(1 + 0.15)^(1/24) − 1] × 100 = 0.58% per month, rounded to two decimal places. Keep the stated numerator, denominator and units distinct. Common errors: using a simple monthly rate instead of compounding gives 0.63 percent per month; dividing by 12 months instead of 24 gives 1.25 percent per month; compounding over 12 periods instead of 24 gives 1.17 percent per month.
Why This Is the Correct Answer
Option A is correct because the compound monthly rate is [(1 + 0.15)^(1/24) - 1] x 100 = 0.58% per month, rounded to two decimal places. Compounding 0.58% for 24 months reproduces the total 15% increase.
Why the Other Options Are Wrong
Option B: 0.63 percent per month
Option B, 0.63 percent per month, comes from a simple rate: 15 / 24 = 0.625, about 0.63. The question asks for a compounded rate, which is (1.15^(1/24) - 1) x 100 = 0.58%.
Option C: 1.17 percent per month
Option C, 1.17 percent per month, comes from compounding over 12 periods instead of 24: (1.15^(1/12) - 1) x 100 = 1.17. The change occurred over 24 months, so the correct rate is (1.15^(1/24) - 1) x 100 = 0.58%.
Option D: 1.25 percent per month
Option D, 1.25 percent per month, comes from dividing 15% by 12 months instead of 24 and without compounding: 15 / 12 = 1.25. The correct compounded rate over 24 months is 0.58%.
Compound means root
To pull a per-period compound rate out of a total change, take the nth root of the growth factor and subtract 1; dividing only works for simple rates.
How to use: Use this rule whenever a question says compounded or constant compound rate.
Exam Tip
A compounded per-period rate is slightly lower than the simple rate for the same total increase, so a simple-division answer slightly higher than yours is a likely distractor.
Common Mistakes to Avoid
- -Dividing the total percentage by the number of months when compounding is specified
- -Using 12 periods when the change spans 24 months
- -Forgetting to subtract 1 from the root of the growth factor
Concept Deep Dive
Analysis
This question tests converting a total price change into a compounded monthly rate. Because the rate compounds, take the 24th root of the total growth factor rather than dividing the percentage by 24. The traps involve simple division and using 12 periods instead of 24.
Background Knowledge
Compounding means each period's change applies to the already-changed value, so the total growth factor equals (1 + monthly rate) raised to the number of months. Solving for the rate requires a root, not division. The same logic underlies future value and present value calculations used in appraisal.
Real-World Application
An appraiser finds matched paired sales showing a 15% increase over two years and wants a monthly time adjustment. Using a compounded rate of about 0.58% per month lets her adjust comparables that sold at different points in that period consistently.
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