Final answer:
The car will take 14 years to depreciate from its initial value of $25,000 to $8,500, assuming it loses $1,250 in value per year. This is calculated by dividing the total depreciation needed ($16,500) by the depreciation rate ($1,250), and rounding up to the nearest whole year.
Step-by-step explanation:
How many years will it take for a new car to be worth $8,500 if it is depreciating at $1,250 per year from an original value of $25,000?
To solve this question, we need to use the concept of linear depreciation, which assumes that a car loses the same amount of value every year. The formula for depreciation is the following:
Final Value = Initial Value - (Depreciation Rate × Number of Years)
In this case, the initial value is $25,000, the depreciation rate is $1,250 per year, and we are solving for the number of years it takes for the car to reach a final value of $8,500.
Applying the values to the formula:
$8,500 = $25,000 - ($1,250 × Number of Years)
Now, we solve for the number of years:
$1,250 × Number of Years = $25,000 - $8,500
$1,250 × Number of Years = $16,500
Number of Years = $16,500 / $1,250
Number of Years = 13.2
Since we cannot have a fraction of a year in this context, we round up to the next whole year. Therefore, it will take 14 years for the car to be worth $8,500. The correct answer is (c) 14 years.