Question

A magazine says that a new car's value drops by 30% in the first year. The car's value then drops by 15% each year after that. Greg says "That means the value of a new car is halved in 3 years." Is Greg correct? Justify your answer.

Answer 1

Yes.

Explanation:

let `x` be the cost of the car when new.

After one year the value drops by `30%`. The value at the start of the second year will be:

`(70)/100x`

The second year the value drops by `15%`. The value at the start of the third year will be:

`85/100*(70)/100x`

In the third year the value drops by `15%`. The value at the end of the third year will be:

`85/100*85/100*(70)/100x=505750/100^3x=2023/4000x=0.50575x=50.58/100x`
`->=50.57%` of `x`

This is very close to `50%`, so the answer is yes.