The car will be worth $16,502.03 after 5 years.
The Breakdown
To calculate the value of the car after 5 years, we can use the formula for exponential decay:
V = P × e^(-rt)
Where:
V = final value of the car
P = initial value of the car
r = depreciation rate (as a decimal)
t = time in years
In this case, the initial value of the car (P) is $24,600 and the depreciation rate (r) is 8% or 0.08. We want to find the value of the car after 5 years (t = 5).
Plugging in these values into the formula, we get:
V = 24600 × e^(-0.08 × 5)
Using a calculator, we can evaluate this expression:
V ≈ 24600 × e^(-0.4)
V ≈ 24600 × 0.67032
V ≈ 16502.032
Therefore, the car will be worth approximately $16,502.03 after 5 years.