Final answer:
To find the value of a car after 4 years with a 6% annual depreciation rate, use the exponential decay formula V = P(1 - r)^n. Here, V would be approximately $3,897.50 after 4 years for a car currently worth $5,000.
Step-by-step explanation:
To calculate the depreciation of a car at a rate of 6% per year, we can use the formula for exponential decay, which is V = P(1 - r)^n, where V is the future value of the car, P is the present value, r is the depreciation rate, and n is the number of years. In this case, the car is worth $5,000 now, so P is $5,000, the depreciation rate r is 0.06 (6% expressed as a decimal), and n is 4 years.
Using the formula, the calculation would be V = $5,000(1 - 0.06)^4
- First, calculate the depreciation factor: 1 - 0.06 = 0.94
- Raise 0.94 to the 4th power: 0.94^4 = 0.7795 (approximately)
- Multiply this factor by the present value of the car: $5,000 x 0.7795 = $3,897.5
Therefore, after 4 years, the car would be worth approximately $3,897.50.