A dwelling is 30 years old but has an estimated effective age of 10 years and a total economic life of 55 years. The current cost new of the improvements is $340,000. What is the depreciation by the straight-line age-life method, to the nearest dollar?
Correct Answer
A) $61,818
340000×10÷55=61818.18. Common errors: using the 30-year actual age instead of the 10-year effective age gives $185,455; reporting the depreciated amount instead of depreciation gives $278,182; dividing by the 45-year remaining life instead of the 55-year total life gives $75,556.
Why This Is the Correct Answer
Option A is correct because $340,000 × 10 ÷ 55 = $61,818.18, which rounds to $61,818. The age-life method divides effective age by total economic life, and the 10-year supported effective age is the proper input rather than the 30-year actual age.
Why the Other Options Are Wrong
Option B: $75,556
Option B is wrong because $75,556 comes from $340,000 × 10 ÷ 45, dividing by the 45-year remaining economic life instead of the 55-year total economic life. The correct ratio is 10 ÷ 55, giving $61,818.
Option C: $185,455
Option C is wrong because $185,455 comes from $340,000 × 30 ÷ 55, using the 30-year actual age instead of the 10-year effective age. Using effective age gives $340,000 × 10 ÷ 55 = $61,818.
Option D: $278,182
Option D is wrong because $278,182 is $340,000 × (1 − 10 ÷ 55), which is the depreciated improvement amount, not the depreciation. The depreciation itself is $340,000 − $278,182 = $61,818.
Effective over total
Age-life depreciation equals effective age over total economic life, times cost new. Actual age and remaining life do not go in this ratio.
How to use: Use this ratio to set up any straight-line age-life depreciation problem before you multiply.
Exam Tip
Check whether the question asks for depreciation or for the depreciated value, since both figures often appear as options.
Common Mistakes to Avoid
- -Using actual age instead of effective age
- -Dividing by remaining economic life instead of total economic life
- -Reporting the depreciated cost when the question asks for depreciation
Concept Deep Dive
Analysis
This question tests the age-life method, which estimates depreciation as effective age divided by total economic life, applied to cost new. The trap is the actual age of 30 years, which is not the input the method uses. The answer is the depreciation amount, not the depreciated cost.
Background Knowledge
In the age-life method, the ratio of effective age to total economic life is applied to cost new to estimate accrued depreciation. Effective age reflects the condition and utility of the improvement and can be less or more than its actual age. Remaining economic life equals total economic life minus effective age.
Real-World Application
An appraiser values a 30-year-old house that was extensively updated and judges its effective age at 10 years. Using a 55-year total economic life, the appraiser applies 10 ÷ 55 to cost new to estimate accrued depreciation.
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