Car decreases in value: $14300 @ 2yrs, $10200 @ 4yrs

[lewysangel]

The value of a car bought in 2000 continues to decrease in value as time passes by. Two years after the car was bought, it was worth $14300; four years after it was bought it was worth $10200. What is the depreciation rate? At this rate, in what year will the value of the car be zero?

 

[jwpaine]

Re: Word Problem

The value of a car bought in 2000 continues to decrease in value as time passes by. Two years after the car was bought, it was worth $14300; four years after it was bought it was worth $10200. What is the depreciation rate? At this rate, in what year will the value of the car be zero?

Two years after the car was bought, it was worth $14300
Four years after it was bought it was worth $10200.


Between year 2 and four the car dropped in price by ($14300 - $10200) = $4100

The car looses $4100/2 = $2050 every year.

The original price of the car is $14300 + 2($2050) = $18400

Let y = years
Price = $18400 - $2050(y)

Now set price = 0 and solve for y

Show ALL work from now on.

 

[TchrWill]

Re: Word Problem

The value of a car bought in 2000 continues to decrease in value as time passes by. Two years after the car was bought, it was worth $14300; four years after it was bought it was worth $10200. What is the depreciation rate? At this rate, in what year will the value of the car be zero?

Given only two data points, I will assume that the decrease in value is linear.
The value loss between the 2nd and 4th years is $4100 or a linear loss of $2050/year.
This implies an original cost of $18,400.
The value after 6 years would be $6100.
The value after 8 years would be $2000.
The value would then be zero at the end of the 9th year.