Question

A new car is purchased for $50,000 and over time it’s value depreciates by one half every 5 years. What is the value of the car 7 years after it was purchased, to the nearest hundred dollars?

Answer 1

The value of the car after 5 years would be $23914.85

Explanation:

Given:

Worth of the new car = $50,000

Every 5 years the value depreciates by 1/2

i.e., every 5 years the value depreciates by 50%

So, we can say that every year the value depreciates by 10%

The worth of the car after 7 years would be

$W = C (1 - \frac{D}{100} )^t$

where,

W is the depreciated value

C is the current value

D is the depreciation rate

t is the time

Substituting the value in the equation we get:

$W = 50000( 1 - \frac{10}{100} )^7\\\\W = 50000 (\frac{9}{10} )^7\\\\W = 23914.85$

Therefore, the value of the car after 5 years would be $23914.85