An improvement has an effective age of 18 years and a total economic life of 45 years. Using the straight-line age-life method, what is the percentage of depreciation?
Correct Answer
A) 40%
18÷45×100 = 40. Common errors: reporting the remaining share instead of depreciation gives 60%; inverting the ratio (45 ÷ 18) gives 250%; dividing by the 27-year remaining life instead of the 45-year total life gives 67%.
Why This Is the Correct Answer
Option A is correct because 18 / 45 x 100 = 40%. The age-life method divides effective age by total economic life, so 40% is the depreciation percentage. The remaining 60% is the percent good.
Why the Other Options Are Wrong
Option B: 60%
Option B is wrong because 60% is the remaining share, (1 - 18/45) x 100 = 60%, not the depreciation. The depreciation is 18 / 45 = 40%.
Option C: 67%
Option C is wrong because 67% comes from dividing by the 27-year remaining life instead of the 45-year total life: 18 / (45 - 18) x 100 = 67%. The correct ratio is 18 / 45 = 40%.
Option D: 250%
Option D is wrong because 250% comes from inverting the ratio: 45 / 18 x 100 = 250%. Depreciation cannot exceed 100% of cost, and the correct figure is 18 / 45 = 40%.
Age over life
Depreciation = Age over Life: effective age on top, total economic life on the bottom. Swap them or use remaining life and the answer goes wrong.
How to use: Use this whenever an age-life question gives effective age and total economic life.
Exam Tip
Before choosing, check that your percentage is the depreciation, not the percent good. A ratio above 100% signals an inverted division.
Common Mistakes to Avoid
- -Reporting the percent good (60%) as the depreciation
- -Dividing by remaining life instead of total economic life
- -Inverting the ratio to total life over effective age
Concept Deep Dive
Analysis
This question tests the age-life method, where accrued depreciation equals effective age divided by total economic life. With an effective age of 18 years and a 45-year total life, the ratio is 18 / 45 = 0.40, or 40%. Watch the order of the division and which life figure goes in the denominator.
Background Knowledge
The age-life (straight-line) method estimates depreciation by dividing effective age by total economic life. Remaining economic life is total life minus effective age, and percent good is the complement of the depreciation percentage.
Real-World Application
An appraiser judges a 25-year-old home to have an effective age of 18 years because of updates, with a 45-year total economic life. The appraiser applies 40% age-life depreciation to the cost new.
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