A cash price of $500,000 occurred 18 months before the effective date. Apply a supported simple 1.5% annual increase on original price, prorated by months. Then add a supported +$25,000 location difference in effective-date dollars. What adjusted price results?
Correct Answer
C) $536,250
500000×(1+0.015×18÷12)+25000=536250. Common errors: leaving out the location adjustment gives $511,250; applying the annual rate to 18 periods instead of 1.5 years gives $660,000; subtracting the location adjustment instead of adding it gives $486,250.
Why This Is the Correct Answer
Option C is correct because 18 months equals 1.5 years, so the simple time increase is 0.015 × 1.5 = 2.25%, and $500,000 × 1.0225 = $511,250. Adding the supported +$25,000 location difference gives $511,250 + $25,000 = $536,250. This combines a percentage adjustment and a dollar adjustment in the order the facts describe.
Why the Other Options Are Wrong
Option A: $486,250
Option A, $486,250, comes from subtracting the location adjustment instead of adding it: $511,250 − $25,000 = $486,250. The location difference is stated as +$25,000, so the correct result is $511,250 + $25,000 = $536,250.
Option B: $511,250
Option B, $511,250, is only the time-adjusted price, $500,000 × (1 + 0.015 × 18 ÷ 12). It leaves out the +$25,000 location adjustment; adding it gives the correct $536,250.
Option D: $660,000
Option D, $660,000, applies the 1.5% annual rate to 18 periods instead of 1.5 years: $500,000 × (1 + 0.015 × 18) + $25,000 = $660,000. Prorating by months gives 0.015 × 1.5 = 2.25%, which leads to $536,250.
Months to years first
Divide months by 12 before multiplying by an annual rate: 18 months is 1.5 years, not 18 periods.
How to use: Use this whenever a time adjustment is quoted as an annual rate but the elapsed time is given in months.
Exam Tip
Check the time unit before multiplying; a result that looks far too large often means months were treated as years. Then confirm the sign of each dollar adjustment.
Common Mistakes to Avoid
- -Multiplying the annual rate by the number of months instead of years
- -Forgetting the location adjustment after the time adjustment
- -Subtracting a positive location adjustment
Concept Deep Dive
Analysis
This question tests a two-step adjustment sequence: a prorated simple time adjustment followed by a dollar location adjustment stated in effective-date dollars. The 18 months must be converted to 1.5 years before applying the 1.5% annual rate to the original price. The +$25,000 location difference is then added to the time-adjusted price.
Background Knowledge
Market conditions (time) adjustments bring a comparable's price from its sale date to the effective date of the appraisal, and they must be supported by evidence. With simple growth, the rate is applied only to the original price and prorated by the fraction of a year elapsed. Percentage and dollar adjustments may be combined, so the sequence and the dollar basis of each adjustment matter.
Real-World Application
An appraiser uses a comparable that sold 18 months ago in a market that analysis shows rose about 1.5% per year. After applying the prorated time adjustment, the appraiser adds a market-supported location adjustment because the subject's location is superior to the comparable's.
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