Question

A new car loses 20% of its original value when you buy it and then 8% of its original value per year, or D = 0.8V − 0.08Vy where D is the value after y years with an original value V.

Answer 1

$37500

Explanation:

A new car loses 20% of its original value when you buy it and 8% of its original value per year . A 6 year old car is worth $12000 what was the original value?

Solution:

Let V represent the original value of the car, and let D be the value of the car after y years.

Immediately the car is bought it has 20% of its initial value, and it loses 8% of its value per year. Hence:

At zero years, (y = 0); D = V - 20% of V = V - 0.2V = 0.8V (it loses 20%)

After y years: D = 0.8V - (8% of V)y = 0.8V - (0.08V)y

From the question, the car is worth $12000 after 6 years. y = 6, D = $12000, we are to find V:

D = 0.8V - (0.08V)y

Substituting:

12000 = 0.8V - (0.08V * 6)

12000 = 0.8V - 0.48V

12000 = 0.32V

V = 12000 / 0.32

V = 37500

V = $37500