Question

PLEASE

Dan's car depreciates at a rate of 12% per year.
By what percentage has Dan's car depreciated after 6 years?
Give your answer to the nearest percent.

Answer 1

Dan's car depreciated by 54% after 6 years.

Explanation:

Price of a depreciating asset:

The price of a depreciating asset after t years is given by:

`P(t) = P(0)(1-r)^(t)`

In which P(0) is the initial price and r is the decrease rate, as a decimal.

Dan's car depreciates at a rate of 12% per year.

This means that
`r = 0.12`, so

`P(t) = P(0)(1-r)^(t)`

`P(t) = P(0)(1-0.12)^(t)`

`P(t) = P(0)(0.88)^(t)`

By what percentage has Dan's car depreciated after 6 years?

Relative to the initial value, the value after 6 years is given by:

`P(6) = P(0)(0.88)^6 = 0.46P(0)`

The value after 6 years if 0.44 of the initial value, that is, there was a depreciation of 100 - 46 = 54%.

Dan's car depreciated by 54% after 6 years.