Question

For tax purposes, a car rental company assumes each car in their fleet depreciates by 10.8% per year. If the initial value of a

car is $20,700.00, what will the value be when the car is 12 years old?

Answer 1

Value ≈ $6,851.73

Explanation:

To calculate the value of the car after 12 years of depreciation, we can use the formula for exponential decay:

Value = Initial Value * (1 - Rate)^Time

In this case, the initial value of the car is $20,700.00 and the depreciation rate is 10.8% or 0.108 (expressed as a decimal). The time is 12 years.

Plugging these values into the formula, we get:

Value = $20,700.00 * (1 - 0.108)^12

Simplifying the calculation:

Value = $20,700.00 * (0.892)^12

Value = $20,700.00 * 0.330578

Value ≈ $6,851.73

Therefore, the value of the car when it is 12 years old, considering a depreciation rate of 10.8% per year, would be approximately $6,851.73.