Question

A new car is purchased for 20800 dollars. the value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 years?

Answer 1

Answer: $4742.10

Explanation:

Exponential depreciation formula :-

`y=A(1-r)^t` , where y is the value of good after t years , r is rate of depreciation and A is the initial value.

Given : A= $20800 ; r=10.75%=0.1075

The equation models this situation:

`y=20800(1-0.1075)^t=20800(0.8925)^t`

Then, the value of car after t=13 years :-

`y=20800(0.8925)^(13)=4742.09507708\approx4742.10`

Hence, the value of car after 13 years = $4742.10