Question

A new car is purchased for 24000 dollars. The value of the car depreciates at 6.75% per year. To the nearest year, how long will it be until the value of the car is 15500 dollars?

Answer 1

Answer:

5.24 years

Step-by-step explanation:

Given: New car purchased for $24000

           rate of depreciation is 6.75%

           Residual value= $15500 .

First, lets find the amount of depreciation over a period of time.

Amount of depreciation=  $\ 24000-\ 15500= \ 8500$

∴ Amount of depreciation = $8500

Lets assume the number of years be "x"

Now, using straight line method to find the number of years to have value of car as $15500.

Amount of depreciation= $\frac{Purchase\ amount\times depreciation\ rate\times time}{100}$

∴  $8500= \frac{24000\times 6.75\times x}{100}$

⇒  $8500= 1620\times x$

dividing both side by 1620

⇒  $x= \frac{8500}{1620}$

∴ x= 5.24 years

Hence, It will take 5.24 years until the value of car is $15500.