Final answer:
The future value of a car purchased for $16,400 that depreciates at 12.5% per year after 8 years is calculated using the formula for exponential decay, resulting in an approximate value of $6,190.40.
Step-by-step explanation:
The student is asking about the depreciation of a car's value over time. To calculate the future value of the car after 8 years, we use the formula for exponential decay, which in this case is the car's value after depreciation. Since the car depreciates at 12.5% per year, we can represent this as 0.125 in decimal form.
The formula to use is:
Future Value = Present Value × (1 - rate of depreciation)^number of years
Plugging the values into the formula, we get:
Future Value = $16,400 × (1 - 0.125)^8
Calculating this, we find:
Future Value = $16,400 × (0.875)^8
Future Value = $16,400 × 0.3773536
Future Value ≈ $6,190.40
The value of the car, to the nearest cent, after 8 years will be approximately $6,190.40.