Final answer:
The value of the car after 5 years, with a 7% annual depreciation rate from an initial purchase price of $20,000, will be approximately $13,966.74.
Step-by-step explanation:
The value of a car after depreciation can be calculated using the formula for exponential decay: V = P(1 - r)^t, where V is the final value, P is the initial value, r is the rate of depreciation, and t is the time in years. In this case, the car was purchased for $20,000 and depreciates at a rate of 7% per year. So, after 5 years, the value V of the car can be calculated as follows:
V = $20,000(1 - 0.07)^5
Calculating this gives us:
V = $20,000(0.93)^5
V = $20,000(0.6983372960937497)
V ≈ $13,966.74
Therefore, the value of the car after 5 years will be approximately $13,966.74.