1 Answer

Divyank · Answer 1 · 2022-10-02T10:51:57+0000

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

$y=a\left(1-(r)/(100)\right)^t$

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

$y=10000\left(1-(5)/(100)\right)^2$

$y=10000\left(1-0.05\right)^2$

$y=10000\left(0.95\right)^2$

On further simplification, we get

y=10000(0.95)(0.95)

y=9025

Therefore, the present value of the car is £9025.

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