A comparable property sold 8 months ago for $425,000. Market analysis indicates property values have been increasing at 0.5% per month. What is the time-adjusted sale price?
Correct Answer
B) $442,000
Time adjustment: $425,000 × (1 + 0.005)^8 = $425,000 × 1.0407 = $442,298, rounded to $442,000. This adjusts the historical sale price to current market conditions.
Why This Is the Correct Answer
Option B correctly applies the compound interest formula: $425,000 × (1 + 0.005)^8 = $425,000 × 1.0407 = $442,298. This calculation accounts for the 0.5% monthly appreciation compounded over 8 months. The result is properly rounded to $442,000, reflecting the time-adjusted value that represents what the comparable would sell for in today's market. This methodology correctly captures the cumulative effect of market appreciation over the 8-month period.
Why the Other Options Are Wrong
Option A: $425,000
Option A represents the original sale price without any time adjustment, ignoring the 8 months of market appreciation at 0.5% per month that has occurred since the sale.
Option C: $408,000
Option C suggests the property has decreased in value, which contradicts the given information that values have been increasing at 0.5% per month.
Option D: $438,125
Option D appears to use simple interest ($425,000 × 1.04 = $442,000) rather than compound interest, failing to account for the compounding effect of monthly appreciation over 8 months.
TIME Compound Formula
TIME = Take Initial Money, Exponentially compound. Remember: (1 + rate)^periods, where the rate is the decimal form (0.5% = 0.005) and periods is the number of time units.
How to use: When you see a time adjustment question, immediately identify: (1) original price, (2) rate per period as decimal, (3) number of periods, then apply (1 + rate)^periods formula.
Exam Tip
Always convert percentages to decimals (0.5% = 0.005) and use the compound interest formula, not simple interest, unless specifically told otherwise.
Common Mistakes to Avoid
- -Using simple interest instead of compound interest
- -Forgetting to convert percentage to decimal form
- -Applying the wrong direction of adjustment (appreciation vs depreciation)
Concept Deep Dive
Analysis
Time adjustments are critical in the sales comparison approach to account for market changes between the sale date of comparable properties and the effective date of the appraisal. This adjustment uses compound interest calculations to reflect how property values have appreciated or depreciated over time. The formula applies the monthly rate of change compounded over the number of months that have elapsed. Time adjustments ensure that historical sales data accurately reflects current market conditions, making comparables truly comparable to the subject property's current value.
Background Knowledge
Time adjustments require understanding compound interest calculations and how market conditions change property values over time. Appraisers must be able to calculate both appreciation and depreciation adjustments using the formula: Adjusted Price = Original Price × (1 ± rate)^periods.
Real-World Application
Appraisers regularly encounter sales that occurred months or even years before the appraisal date, requiring time adjustments based on market trend analysis from MLS data, assessor records, and local market studies to ensure accurate valuations.
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