Final answer:
The resale value of a car bought for $20,000 and depreciating at 10% annually is calculated by repeatedly reducing the value by 10%. After five years, the car's value will be $11,809.80.
Step-by-step explanation:
The resale value of a car that was purchased new for $20,000 and depreciates by 10% each year can be calculated using the formula for exponential decay. This question overlooks the information regarding maintenance costs and focuses on determining the depreciation of the car's value over time.
Each year, the car's value depreciates to 90% of its value from the previous year, which means we multiply the current value by 0.9 to get the next year's value. To find the value after 5 years, we apply this depreciation factor five times:
- Year 1: $20,000 x 0.9 = $18,000
- Year 2: $18,000 x 0.9 = $16,200
- Year 3: $16,200 x 0.9 = $14,580
- Year 4: $14,580 x 0.9 = $13,122
- Year 5: $13,122 x 0.9 = $11,809.80
Therefore, the resale value of the car after 5 years would be $11,809.80.