Question

Colin buys a car for £31300.

It depreciates at a rate of 2% per year.
How much will it be worth in 4 years?
Give your answer to the nearest penny where appropriate.​

Answer 1

The car will be worth £28,870.12 in 4 years

Explanation:

The equation for the value of the car after t years has the following format:

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

In which V(0) is the current value, and r is the annual constant depreciation rate.

Colin buys a car for £31300. It depreciates at a rate of 2% per year.

This means that
`V(0) = 31300, r = 0.02`

So

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

`V(t) = 31300(1-0.02)^(t)`

`V(t) = 31300(0.98)^(t)`

How much will it be worth in 4 years?

This is V(4).

`V(t) = 31300(0.98)^(t)`

`V(4) = 31300(0.98)^(4) = 28870.12`

The car will be worth £28,870.12 in 4 years