An improvement has a total economic life of 60 years and an effective age of 18 years. What is its remaining economic life?
Correct Answer
B) 42 years
60−18=42 years; 42÷60=0.70 remaining fraction. Common errors: adding effective age to total life instead of subtracting gives 78 years; reporting the effective age instead of the remaining life gives 18 years; reporting the 70% remaining fraction as years gives 70 years.
Why This Is the Correct Answer
Option B is correct because remaining life is 60 − 18 = 42 years. The matching remaining fraction is 42 ÷ 60 = 0.70. Effective age and remaining life together make up the 60-year total life.
Why the Other Options Are Wrong
Option A: 18 years
Option A, 18 years, is the effective age itself, not the remaining life. Remaining life is 60 − 18 = 42 years.
Option C: 70 years
Option C, 70 years, treats the 70% remaining fraction (42 ÷ 60 = 0.70) as a number of years. The remaining life is 42 years.
Option D: 78 years
Option D, 78 years, adds effective age to total life (60 + 18) instead of subtracting it. Remaining life is 60 − 18 = 42 years.
Age plus remaining equals total
Effective age plus remaining economic life equals total economic life, so subtract to find either missing piece.
How to use: Use this identity whenever one of the three age-life terms is missing.
Exam Tip
Keep units straight: remaining life is in years, while the remaining fraction is a ratio or percentage.
Common Mistakes to Avoid
- -Adding effective age to total life
- -Reporting a percentage as a number of years
- -Confusing effective age with remaining life
Concept Deep Dive
Analysis
This question tests the age-life identity: total economic life equals effective age plus remaining economic life. Subtracting effective age from total life gives remaining life. The matching remaining fraction is remaining life divided by total life.
Background Knowledge
In the age-life model, total economic life is the sum of effective age and remaining economic life. The ratio of effective age to total life is the depreciation percentage, and the ratio of remaining life to total life is percent good.
Real-World Application
An appraiser estimates a home's total economic life at 60 years and its effective age at 18 years based on condition. The appraiser reports a remaining economic life of 42 years, consistent with that effective age.
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