Using the straight-line method, a building with a 50-year economic life that is 15 years old has what percentage of depreciation?
Correct Answer
A) 30%
Straight-line depreciation = (Age ÷ Economic Life) × 100. 15 years ÷ 50 years = 0.30 or 30% depreciation.
Why This Is the Correct Answer
Option A (30%) is correct because the straight-line depreciation formula is Age ÷ Economic Life × 100. With a 15-year-old building having a 50-year economic life, the calculation is 15 ÷ 50 = 0.30 or 30%. This represents the percentage of the building's useful life that has been consumed through aging. The remaining 70% represents the building's remaining economic life.
Why the Other Options Are Wrong
Option B: 70%
Option B (70%) represents the remaining useful life percentage, not the depreciation percentage. This is calculated as (Economic Life - Age) ÷ Economic Life, which would be (50-15) ÷ 50 = 70%. This is the complement of depreciation, showing how much useful life remains rather than how much has been lost.
Option C: 15%
Option C (15%) simply states the age of the building in years without converting it to a percentage of the economic life. This fails to account for the total economic life span and doesn't represent a percentage calculation at all.
Option D: 35%
Option D (35%) appears to be an arbitrary number that doesn't result from any standard depreciation calculation method. It may represent a calculation error or confusion with other depreciation methods, but it's not the result of the straight-line formula.
Age Over Life = Depreciation Strife
Remember 'AOL' - Age Over Life = percentage of depreciation. Think of the old AOL internet service that got slower (depreciated) over time as a percentage of its useful period.
How to use: When you see a straight-line depreciation question, immediately think 'AOL' and set up the fraction: building's current Age Over its economic Life, then convert to percentage.
Exam Tip
Always double-check that you're calculating depreciation (what's been lost) rather than remaining useful life (what's left) - these are complementary percentages that add up to 100%.
Common Mistakes to Avoid
- -Calculating remaining useful life instead of depreciation
- -Using chronological age instead of effective age
- -Forgetting to convert the decimal to a percentage
Concept Deep Dive
Analysis
This question tests understanding of the straight-line depreciation method, which is the most basic approach to calculating physical deterioration in real estate appraisal. The straight-line method assumes that a building depreciates at a constant rate over its economic life, making it a simple mathematical calculation. This method divides the current age of the building by its total economic life to determine what percentage of the building's useful life has been consumed. While this method is straightforward, it may not always reflect actual market conditions or the true condition of a property.
Background Knowledge
Straight-line depreciation is one of three primary methods used in real estate appraisal to estimate physical deterioration, alongside the age-life method and the breakdown method. Economic life refers to the period over which a building is expected to contribute to property value, which may differ from its physical life or accounting life.
Real-World Application
Appraisers use straight-line depreciation for cost approach valuations, particularly for newer buildings or when detailed condition analysis isn't available. For example, when appraising a 10-year-old office building with a 40-year economic life, an appraiser would apply 25% depreciation to the reproduction cost new.
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