An improvement has an actual age of 25 years, an effective age of 18 years and a total economic life of 55 years. Using straight-line age-life depreciation, what is the depreciation percentage, to one decimal place?
Correct Answer
A) 32.7%
18÷55×100 = 32.73. Common errors: using actual age instead of effective age gives 45.5%; reporting percent good instead of depreciation gives 67.3%; dividing by remaining economic life instead of total life gives 48.6%.
Why This Is the Correct Answer
Option A is correct because 18 ÷ 55 = 0.3273, or 32.7% when rounded to one decimal. The effective age of 18 years is used rather than the actual age of 25. The denominator is total economic life of 55 years.
Why the Other Options Are Wrong
Option B: 45.5%
Option B, 45.5%, uses actual age instead of effective age: 25 ÷ 55 = 45.5%. The age-life method uses effective age, giving 18 ÷ 55 = 32.7%.
Option C: 48.6%
Option C, 48.6%, divides effective age by remaining economic life: 18 ÷ (55 − 18) = 18 ÷ 37 = 48.6%. The denominator should be total economic life, giving 18 ÷ 55 = 32.7%.
Option D: 67.3%
Option D, 67.3%, is percent good, (55 − 18) ÷ 55 = 67.3%, not depreciation. Depreciation is 18 ÷ 55 = 32.7%.
Effective age over total life
The age-life percentage is effective age divided by total economic life. Subtract it from 100% to get percent good.
How to use: Use this to compute depreciation percentages and to spot the percent good distractor.
Exam Tip
When both actual and effective age are given, the age-life method uses effective age. Check whether the answer wanted is depreciation or percent good.
Common Mistakes to Avoid
- -Using chronological age instead of effective age
- -Dividing by remaining economic life
- -Reporting percent good as the depreciation percentage
Concept Deep Dive
Analysis
This question tests the age-life depreciation percentage. Effective age, not actual age, is divided by total economic life. The result is expressed as a percentage and rounded to one decimal.
Background Knowledge
Under the age-life method, depreciation is estimated by dividing effective age by total economic life. Effective age reflects the property's condition and utility and may differ from its chronological age.
Real-World Application
An appraiser inspects a 25-year-old home that has been well updated and estimates its effective age at 18 years. Using a 55-year total economic life, the appraiser applies about 32.7% depreciation to cost new.
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