A comparable’s cash-equivalent price is $268,000. Evidence supports a simple, noncompounded 0.25% downward adjustment per month, based on the original price, for a verified 8-month contract-to-effective-date interval. What adjusted price results?
Correct Answer
B) $262,640
268000 × [1 + (-0.0025 × 8)] = 262640. The signed change is -5360; compound growth is a different convention. Common errors: compounding instead of using the simple rate gives $262,687; adjusting upward instead of downward gives $273,360; reporting only the signed change gives −$5,360.
Why This Is the Correct Answer
Option B is correct because a simple monthly rate applied to the original price gives $268,000 x [1 + (-0.0025 x 8)] = $268,000 x 0.98 = $262,640. The signed change is -$5,360. The stem specifies a simple, noncompounded rate based on the original price, so compounding does not apply.
Why the Other Options Are Wrong
Option A: $262,687
Option A is wrong because $262,687 comes from compounding the monthly rate instead of applying it simply to the original price. The stem specifies a simple rate: $268,000 x (1 - 0.0025 x 8) = $262,640.
Option C: $273,360
Option C is wrong because $273,360 adjusts upward: $268,000 x (1 + 0.0025 x 8) = $273,360. The evidence supports a downward adjustment, giving $262,640.
Option D: −$5,360
Option D is wrong because -$5,360 is only the signed change, $268,000 x 0.02. The question asks for the adjusted price, $268,000 - $5,360 = $262,640.
Simple means multiply once
For a simple rate, multiply the monthly rate by the months, then apply once to the original price. Compounding repeats the rate on each new total.
How to use: Use this to choose the right method whenever a time adjustment question says simple or noncompounded.
Exam Tip
Check three things in time adjustment questions: simple or compound, upward or downward, and whether the answer asks for the price or the change.
Common Mistakes to Avoid
- -Compounding a rate the evidence defines as simple
- -Adjusting upward in a declining market
- -Reporting the dollar change instead of the adjusted price
Concept Deep Dive
Analysis
This question tests a simple (noncompounded) time adjustment. The rate is -0.25% per month on the original price for 8 months, a total of -2%: $268,000 x (1 - 0.0025 x 8) = $262,640. The distractors reflect compounding, a reversed direction, and reporting only the change.
Background Knowledge
Market conditions (time) adjustments reflect changes in prices between a comparable's contract date and the effective date. Fannie Mae requires time adjustments, or the lack of them, to be supported by evidence. With simple rates, each period's change is based on the original amount; compounding applies changes to the running total.
Real-World Application
Resale data in a softening market show prices falling about a quarter percent per month. An appraiser adjusts an 8-month-old comparable downward by 2% of its price and cites the resale evidence supporting the rate.
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