Question

A new car is purchased for 25000 dollars. The value of the car depreciates at 8.25% per year. What will the value of the car be, , after 15 years?

Answer 1

Given:

Price of a new car = 25000

Depreciation rate = 8.25% = 0.0825

Time = 15 years.

To find:

The value of the car after 15 years.

Solution:

The exponential decay model is

$y=a(1-r)^t$

Where, a is the initial value, r is the rate of decay and t is number of years.

Putting a=25000, r=0.0825 and t=15 in the above formula.

$y=25000(1-0.0825)^{15}$

$y=25000(0.9175)^{15}$

$y=25000(0.274847)$

$y=6871.175$

Therefore, the value of the car after 15 years will be 6871.175.