Respuesta :
Answer:
The smallest possible number of years for the depreciation value of car is 7 years .
Step-by-step explanation:
Given as :
The purchased price of car = $26000
The depreciation rate of car every year = r = 30%
The reduced price of car after n years = $2200 or less
Let The time period for the depreciation value = n years
Now, According to question
The reduced price of car after n years = The purchased price of car × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, $2200 = $26000 × [tex](1-\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, [tex]\dfrac{2200}{26000}[/tex] = [tex](1-\dfrac{\textrm 30}{100})^{\textrm n}[/tex]
Or, 0.084615 = [tex](0.7)^{n}[/tex]
Now, Taking Log both side
So, [tex]Log_{10}[/tex]0.084615 = [tex]Log_{10}[/tex]( [tex](0.7)^{n}[/tex])
Or, -1.07255 = n [tex]Log_{10}[/tex]0.7
Or, -1.07255 = n ( - 0.15490 )
∴ n = [tex]\dfrac{1.07255}{0.15490}[/tex]
I.e n = 6.92 ≈ 7 years
So, Time period for depreciation of car value = n = 7 years
Hence The smallest possible number of years for the depreciation value of car is 7 years . Answer
The year in which the car would be worth 2200 or less is 9 years.
What is the year in which the car would worth at most 2200?
When a car loses its value, it means that the price of the car falls with the passage of time.
Number of years = (In FV / PV) r
- FV = future value
- PV = present value
- r = depreciation rate
(in 26,000 / 2200) / 0.3 = 8.2 years = 9 years
To learn more about how to determine the number of years, please check: https://brainly.com/question/21841217
