Question

A car vehicle price history for a certain make and model contains the following list of yearly price values:

$21,000 $18,900 $17,010 $15,309 $13,778.1 $12,400.29
The original price of the car was $21,000. It exponentially depreciated to $18,900 after 1 year and continued depreciating by the same percentage each year thereafter. What
will the value of the car be after 8 years?

Answer 1

$9,039.81

Explanation:

Given the exponentially decaying price history of a vehicle as $21,000; $18,900; $17,010; $15,309; $13,778.10; $12,400.29; you want to know the value after 8 years of depreciation at the same rate.

Value equation

The multiplier of value each year is 18900/21000 = 0.9. This means the value of the vehicle can be represented by the price function ...

price = (initial price) · 0.9^t

where t is the number of years the vehicle has depreciated.

After 8 years, the value will be ...

price = $21000·0.9^8 ≈ $9,039.81

After 8 years, the value of the car will be $9,039.81.