Using the age-life method, what is the percentage of accrued depreciation for a 15-year-old building with a total economic life of 50 years?
Correct Answer
A) 30%
Age-life depreciation percentage = Actual Age ÷ Total Economic Life. 15 years ÷ 50 years = 0.30 or 30%.
Why This Is the Correct Answer
Option A (30%) is correct because the age-life method formula is straightforward: Actual Age ÷ Total Economic Life = Depreciation Percentage. In this case, 15 years ÷ 50 years = 0.30 or 30%. This means the building has depreciated 30% of its total value based on age alone. The calculation assumes linear depreciation, where each year represents 2% depreciation (100% ÷ 50 years = 2% per year), and after 15 years, the total depreciation is 15 × 2% = 30%.
Why the Other Options Are Wrong
Option B: 70%
Option B (70%) represents the remaining economic life percentage, not the accrued depreciation. This is calculated as (Total Economic Life - Actual Age) ÷ Total Economic Life = (50-15) ÷ 50 = 70%. This shows how much useful life remains, but the question specifically asks for accrued depreciation.
Option C: 15%
Option C (15%) incorrectly uses just the actual age as a percentage without dividing by the total economic life. This is a common error where test-takers confuse the numerator (15 years) with the final percentage calculation.
Option D: 50%
Option D (50%) has no mathematical basis in this problem and may represent confusion with the total economic life figure or an arbitrary guess. This percentage would only be correct if the building were 25 years old (25 ÷ 50 = 50%).
The Age-Life Fraction
Remember 'A over E equals D' - Actual age over Economic life equals Depreciation percentage. Visualize a fraction: the top number is how old it is, the bottom number is how long it should last, and the result is how much it has depreciated.
How to use: When you see an age-life depreciation question, immediately set up the fraction: actual age on top, total economic life on bottom, then convert to percentage. Always check that your answer is less than 100% and makes logical sense.
Exam Tip
Double-check your calculation by working backwards: if 30% is depreciated, then 70% remains, and 70% of 50 years equals 35 years remaining, which added to 15 years used equals 50 years total.
Common Mistakes to Avoid
- -Calculating remaining life percentage instead of depreciation percentage
- -Using actual age as the final percentage without dividing by economic life
- -Confusing economic life with physical life or chronological age
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in the cost approach to real estate valuation. This method assumes that depreciation occurs at a steady, linear rate over the economic life of a building. The concept tests an appraiser's ability to calculate accrued depreciation as a percentage by comparing the actual age of a structure to its total economic life. Understanding this method is crucial because it provides a baseline estimate for physical deterioration and functional obsolescence in older buildings.
Background Knowledge
The age-life method assumes that buildings depreciate in a straight-line fashion over their economic life, which is the period during which the building contributes to property value. Economic life differs from physical life because it considers when a building becomes economically obsolete, not just physically deteriorated.
Real-World Application
Appraisers use the age-life method as a starting point for depreciation analysis, particularly for residential properties. However, in practice, they often adjust this figure based on actual condition, maintenance quality, and market factors, as real depreciation rarely follows a perfectly linear pattern.
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