Given:
The value of car before two years = £10000
The value of the car decreases by 5% each year.
To find:
The present value of the car.
Solution:
The exponential decay model for present value is
[tex]y=a\left(1-\dfrac{r}{100}\right)^t[/tex]
Where, a is the initial value, r is the rate of decay and t is time in years.
Putting P=10000, r=5 and t 2, we get
[tex]y=10000\left(1-\dfrac{5}{100}\right)^2[/tex]
[tex]y=10000\left(1-0.05\right)^2[/tex]
[tex]y=10000\left(0.95\right)^2[/tex]
On further simplification, we get
[tex]y=10000(0.95)(0.95)[/tex]
[tex]y=9025[/tex]
Therefore, the present value of the car is £9025.
