A building has an effective age of 15 years and a remaining economic life of 35 years. Using the age-life method, what is the percentage of accrued depreciation?
Correct Answer
A) 30%
Total economic life = 15 + 35 = 50 years. Accrued depreciation = Effective age ÷ Total economic life = 15 ÷ 50 = 0.30 or 30%.
Why This Is the Correct Answer
The age-life method calculates accrued depreciation by dividing effective age by total economic life. Total economic life equals effective age plus remaining economic life (15 + 35 = 50 years). Accrued depreciation percentage = 15 ÷ 50 = 0.30 or 30%. This represents the portion of the building's useful life that has already been consumed through wear, tear, and obsolescence.
Why the Other Options Are Wrong
Option B: 43%
43% would result from incorrectly calculating 15 ÷ 35, using only the remaining economic life as the denominator instead of the total economic life. This ignores the fundamental principle that depreciation is measured against the entire useful life of the property, not just the remaining portion.
Option C: 57%
57% represents the remaining value percentage (35 ÷ 50), not the accrued depreciation. This is the complement of depreciation - what's left of the building's economic life. Students sometimes confuse depreciation percentage with the remaining useful life percentage.
Option D: 70%
70% has no mathematical basis in this problem and would require an effective age of 35 years with a total life of 50 years. This appears to be a distractor answer with no logical connection to the given data.
Memory Technique
Remember 'DART': Depreciation = Age ÷ Total life. Think 'Age over All' - effective age goes over the total economic life (effective + remaining).
Exam Tip
Always identify total economic life first by adding effective age and remaining economic life, then divide effective age by this total.
Common Mistakes to Avoid
- -Using remaining life instead of total life as denominator
- -Confusing depreciation percentage with remaining value percentage
- -Forgetting to add effective age and remaining life to get total economic life
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