Question

A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to half its original value in 4 years. If you bought a car 8 years ago and it is now worth $5000, how much did you pay for the car originally

Answer 1

Original price of car = $20,000

Explanation:

Let the original price of the car be 'x' dollars.

Given:

Here, the depreciation of the car is occuring exponentially as the value depreciates to half in every four years.

Worth of car after 8 years = $5000

Value after depreciation in 4 years = Half of original value =
`(x)/(2)`

So, value of car after depreciation in another 4 years = Half of the value after 4 years =
`(1)/(2)((x)/(2))=(x)/(4)`

Therefore, final depreciated value after 8 years is
`(x)/(4)`.

But, as per question, final depreciated value is $5000. Thus,

`(x)/(4)=5000\\x=5000* 4\\x=20000`

Therefore, the original price of the car was $20,000.