Answer:
The car will be worth £28,870.12 in 4 years
Step-by-step explanation:
The equation for the value of the car after t years has the following format:
[tex]V(t) = V(0)(1-r)^{t}[/tex]
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 [tex]V(0) = 31300, r = 0.02[/tex]
So
[tex]V(t) = V(0)(1-r)^{t}[/tex]
[tex]V(t) = 31300(1-0.02)^{t}[/tex]
[tex]V(t) = 31300(0.98)^{t}[/tex]
How much will it be worth in 4 years?
This is V(4).
[tex]V(t) = 31300(0.98)^{t}[/tex]
[tex]V(4) = 31300(0.98)^{4} = 28870.12[/tex]
The car will be worth £28,870.12 in 4 years
