Question

A new car is purchased for $40,000 and over time its value depreciates by one half every 3 years. What is the value of the car 17 years after it was purchased, to the nearest hundred dollars?

Answer 1

Value of the car after depreciation = $800.

Explanation:

Formula to get the final value of the car after depreciation of the car price,

Final value =
`\text{Initial value}(1-(r)/(100))^{(t)/(n) }`

Here, t = Number of years after the purchase

n = Number of years for the depreciation of price by half

By substituting values in the formula,

Final value =
`40000(1-(50)/(100))^{(17)/(3)}`

=
`40000(0.5)^{(17)/(3)}`

= $787.451

≈ $800 [Nearest hundred dollars]

Therefore, after 17 years value of the new car will be $800.