A car with an original value of 52,500 depreciates 10,000 in the first year and thereafter...
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A car with an original value of $52,500 depreciates $10,000 in the first year and thereafter at the rate of 8% of the original cost per year. What is its value after 8 years?
Show answer & explanation
The car depreciates $10,000 in year 1, then 8% of $52,500 ($4,200) per year for the remaining 7 years. Total depreciation: $10,000 + (7 × $4,200) = $10,000 + $29,400 = $39,400. Final value: $52,500 − $39,400 = $13,100.
Step-by-step Derivation:
Step 1: Calculate depreciation in year 1 = $10,000
Step 2: Calculate annual depreciation for years 2–8 = 8% × $52,500 = 0.08 × $52,500 = $4,200 per year
Step 3: Number of years at 8% rate = 8 − 1 = 7 years
Step 4: Total depreciation for years 2–8 = 7 × $4,200 = $29,400
Step 5: Total depreciation over 8 years = $10,000 + $29,400 = $39,400
Step 6: Value after 8 years = $52,500 − $39,400 = $13,100.00