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= [tex]\$ 24000-\$ 15500= \$ 8500[/tex]
∴ 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= [tex]\frac{Purchase\ amount\times depreciation\ rate\times time}{100}[/tex]
∴ [tex]8500= \frac{24000\times 6.75\times x}{100}[/tex]
⇒ [tex]8500= 1620\times x[/tex]
dividing both side by 1620
⇒ [tex]x= \frac{8500}{1620}[/tex]
∴ x= 5.24 years
Hence, It will take 5.24 years until the value of car is $15500.
