A cash-equivalent comparable price is $400,000. Market evidence supports a simple 2% annual upward adjustment based on that original price for the verified 18 month contract-to-effective-date interval. What time-adjusted price results?
Correct Answer
B) $412,000
The stipulated simple rate is 2% per year for 18/12 = 1.5 years, giving 3% of the original $400,000. Adjusted price = 400000 × 1.03 = $412,000. The other prices reflect a 3% decrease in place of the supported increase, or unsupported 4% or 6% total increases, not the given simple 3%. Compound annual growth over 1.5 years would be a different formula and would not produce $424,000.
Why This Is the Correct Answer
Option B is correct because 18 months equals 1.5 years, and 2% per year times 1.5 years gives a simple 3% total increase. Applying that to the original price gives $400,000 × 1.03 = $412,000. The stem states the rate is simple and based on the original price, so no compounding is involved.
Why the Other Options Are Wrong
Option A: $388,000
Option A, $388,000, applies the 3% adjustment downward: $400,000 × 0.97 = $388,000. Market evidence supports an upward adjustment, so the result is $400,000 × 1.03 = $412,000.
Option C: $416,000
Option C, $416,000, reflects a 4% increase ($400,000 × 1.04), as if the 18 months were rounded up to 2 full years at 2% each. The interval is 1.5 years, so the correct increase is 3%, giving $412,000.
Option D: $424,000
Option D, $424,000, reflects a 6% increase ($400,000 × 1.06), such as applying the full 2% to each of three 6-month periods. The 2% rate is annual, so 1.5 years gives 3% and $412,000; compounding 2% annually would also not produce $424,000.
Convert months to years first
Divide months by 12 before multiplying by an annual rate: 18 months is 1.5 years, so 2% becomes 3%.
How to use: Use this conversion whenever an annual rate meets a period stated in months.
Exam Tip
Check whether the rate is annual or monthly and whether it is simple or compound before calculating; each answer choice usually matches one of those mix-ups.
Common Mistakes to Avoid
- -Adjusting downward when the market evidence supports an increase
- -Rounding a fractional period up to whole years
- -Treating an annual rate as if it applied to each shorter sub-period
- -Compounding when the stem specifies a simple rate
Concept Deep Dive
Analysis
This question tests a simple (noncompounded) time adjustment over a period that is not a whole number of years. The annual rate must be scaled to the actual interval: 18 months is 1.5 years, so 2% per year gives a 3% total increase applied to the original price. The distractors come from adjusting in the wrong direction, rounding the period up, or applying the annual rate to shorter sub-periods.
Background Knowledge
A simple time adjustment applies a rate to the original price in proportion to elapsed time, without compounding. The elapsed time should be measured over a verified interval, here from the contract date to the effective date. The rate itself must be supported by market evidence.
Real-World Application
An appraiser in a slowly rising market uses an 18-month-old sale because it is the closest match to the subject. Resales in the area support a 2% simple annual increase. The appraiser applies 3% to the $400,000 price and reports an adjusted price of $412,000.
More Sales Comparison Questions
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Improvement cost new is $450,000. Separately supported improvement depreciation deductions of $45,000, $25,000, $15,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $125,000, already reflecting any site losses. What total indicated value results?
Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
Improvement cost new is $800,000. Separately supported improvement depreciation deductions of $120,000, $80,000, $40,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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Which highest-and-best-use criterion addresses whether a proposed use is allowed by zoning and applicable legal restrictions?
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When reconciling value indications from the three approaches to value, an appraiser should:
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