A cash-equivalent comparable price is $480,000. Market evidence supports compounding an upward 1% adjustment for each of 4 complete monthly periods between its contract date and the effective date. What adjusted price results to the nearest dollar?
Correct Answer
B) $499,490
480000 × (1 + 0.01)^4 = 499489.9248. Compound the stated period rate; a simple rate would instead multiply the original base by total periods.
Why This Is the Correct Answer
Option B is correct because compounding 1% for 4 periods gives $480,000 × (1.01)^4 = $480,000 × 1.04060401 = $499,489.92, which rounds to $499,490. The stem specifies compounding, so each period's increase applies to the already adjusted price.
Why the Other Options Are Wrong
Option A: $499,200
Option A, $499,200, uses simple growth: $480,000 × (1 + 0.01 × 4) = $480,000 × 1.04. The stem requires compounding, which gives $480,000 × (1.01)^4 = $499,490.
Option C: $461,086
Option C, $461,086, compounds the 1% in the wrong direction: $480,000 × (0.99)^4 = $461,086. The market evidence supports an upward adjustment, so the correct result is $480,000 × (1.01)^4 = $499,490.
Option D: $19,490
Option D, $19,490, is only the dollar amount of the adjustment ($499,490 - $480,000), not the adjusted price. The question asks for the adjusted price, $499,490.
Compound means power
Simple growth multiplies the rate by the periods; compound growth raises one plus the rate to the power of the periods.
How to use: Use this to pick the right formula when a stem says simple or compound.
Exam Tip
If two answers are very close, one is likely simple growth and the other compound; match the method named in the stem.
Common Mistakes to Avoid
- -Using simple growth when the stem specifies compounding
- -Reporting the dollar adjustment instead of the adjusted price
- -Applying the rate downward when the market is rising
Concept Deep Dive
Analysis
This question tests compounding a monthly time adjustment. With compounding, each month's 1% applies to the previous month's adjusted price, so the multiplier is 1.01 raised to the fourth power. The distractors reflect simple interest, compounding downward and reporting only the dollar change.
Background Knowledge
Time adjustments may be applied as simple rates on the original price or as compound rates on the cumulative adjusted price, depending on what the market evidence supports. Fannie Mae requires that time adjustments, or the lack of them, be supported by evidence. Compounding produces a slightly larger result than simple growth over the same periods.
Real-World Application
In a rapidly appreciating suburb, an appraiser's analysis of repeat sales supports about 1% price growth per month compounded. A comparable sold 4 months before the effective date for $480,000. The appraiser adjusts it to about $499,490 and documents the supporting data.
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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The appraiser of a 2,100-square-foot two-story house with four bedrooms has analyzed two sales: a dated 1,750-square-foot home that sold for $412,000 and is inferior, and a 2,600-square-foot home with a pool that sold for $498,000 and is superior. Closed sales of two-story homes of 1,950 to 2,300 square feet in the same subdivision during the past six months have not yet been reviewed. How should the appraiser narrow the bracket?
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A comparable closed nine months ago; public records show it, but the parties will not discuss terms. Before relying on it, the appraiser should: