A comparable price is $360,000. Increase it by 6%, then reduce the resulting subtotal by 3%. Both percentage bases are expressly specified; no fixed-dollar adjustments apply. What final price results?
Correct Answer
A) $370,152
360000 × 1.06 × 0.97 = 370152; these two pure multiplicative factors commute, while adding percentages would give a different result. Common errors: netting the two percentages to +3% instead of applying them in sequence gives $370,800; leaving out the 3% reduction gives $381,600; dividing by 0.97 instead of multiplying gives $393,402.
Why This Is the Correct Answer
Option A is correct because $360,000 × 1.06 = $381,600, and $381,600 × 0.97 = $370,152. Because both are pure multiplicative factors, the order does not change the result, but netting them into a single +3% would. The stem expressly sets the second base as the subtotal after the first adjustment.
Why the Other Options Are Wrong
Option B: $370,800
Option B, $370,800, is wrong because it nets the two percentages to +3% instead of applying them in sequence: $360,000 × 1.03 = $370,800. The correct calculation is $360,000 × 1.06 × 0.97 = $370,152.
Option C: $381,600
Option C, $381,600, is wrong because it leaves out the 3% reduction: $360,000 × 1.06 = $381,600. Reducing that subtotal by 3% gives $381,600 × 0.97 = $370,152.
Option D: $393,402
Option D, $393,402, is wrong because it divides by 0.97 instead of multiplying: $360,000 × 1.06 ÷ 0.97 = $393,402. A 3% reduction means multiplying by 0.97, which gives $370,152.
Sequential percents multiply, not add
When each percentage applies to the new subtotal, multiply the factors: 1.06 × 0.97. Adding +6% and −3% to get +3% ignores the changing base.
How to use: Use this when a question says a later percentage applies to the subtotal after an earlier adjustment.
Exam Tip
Read which base each percentage uses; if the base changes, chain the multipliers rather than netting the percentages.
Common Mistakes to Avoid
- -Adding and subtracting the percentages into one net figure
- -Dropping the second adjustment
- -Dividing by the reduction factor instead of multiplying
Concept Deep Dive
Analysis
This question tests applying successive percentage adjustments when each percentage has a stated base. The 6% increase applies to $360,000, and the 3% decrease applies to the resulting subtotal. Multiplying the factors gives the answer, while adding the percentages does not.
Background Knowledge
Percentage adjustments can be applied to the original price or sequentially to a running subtotal, and the two methods give different results. The base for each percentage must be stated or supported, since sequential percentages compound rather than simply add.
Real-World Application
An appraiser supports an upward market-conditions adjustment on a comparable's sale price and then a downward location adjustment that her data measured against the time-adjusted price. She applies them in sequence and states the base of each in the grid comments.
More Sales Comparison Questions
Supported adjustments are: non-market financing $10,000, GLA $36/sf, garage $3,500 per car, pool/spa $12,500. A comparable identical to the 2,800 sf subject sold for $267,000 with non-market financing. What is its adjusted price?
Using GLA $36/sf and non-market financing $10,000: a 3,100 sf comparable sold for $277,000 with non-market financing; the subject has 2,800 sf. Bath count differences are not adjusted. What is the adjusted price?
Using garage $3,500 per car and pool/spa $12,500: a comparable with a 2-car garage and a pool/spa sold for $268,000. The subject has a 3-car garage and no pool. What is the adjusted price?
Using GLA $36/sf, garage $3,500 per car and pool/spa $12,500: a 2,600 sf comparable with a 2-car garage and a pool/spa sold for $264,000. The subject is 2,800 sf with a 3-car garage and no pool. What is the adjusted price?
In a neighborhood with declining values and marketing times over six months, what must Fannie Mae lenders confirm about the sales comparison analysis?
A house is a 4,000 square foot home in an area of 2,000 square foot homes. How must the appraiser treat this over-improvement in the sales comparison grid?
According to the Interagency Appraisal and Evaluation Guidelines, which items should an appraisal’s market conditions discussion include?
A comparable listed at $420,000 and sold for $399,000. What sale-to-list price ratio (sale price ÷ list price) does this indicate?
An appraiser wants to describe the neighborhood boundaries in a Fannie Mae report. Which approach is acceptable?
Which of these is listed by Fannie Mae as a sales or financing concession?
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In a market where 40% of transactions close with seller concessions averaging 2%, a comparable with no concessions:
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Comparable 1, a two-story home, sold for $465,000. The buyer assumed the seller's loan, which had a $260,000 balance at 4.5% interest with 180 monthly payments remaining, when new loans carried 6.5%. The buyer's payment is $276 a month less than on a new $260,000 loan at the market rate. The seller had originally borrowed $320,000. Paired sales in the subdivision over the past year show that homes sold with assumable low-rate loans of similar balance and remaining term brought about $12,000 more than similar homes bought with new market-rate loans. What amount should the appraiser deduct from Comparable 1's price for the financing?