Respuesta :
Honda : 16,000
each year depreciates 8% from 100% so will be left with 100-8 =92% or 0.92
in 5 years : 16,000* 0.92^5 ≈ $10,545.30
in 10 years : 16,000* 0.92^10 ≈ $6,950.22
Kia : $12,000
each year depreciates 12 % from 100% so will be left with 100-12 =88% or 0.88
in 5 years : 12,000* 0.88^5 ≈ $6,332.78
in 10 years : 12,000* 0.88^10 ≈ $3,342.01
Jess should buy the Honda if wants to use it for 5 years or less because although is more expensive than Kia, it depreciates less in 5 years.
In 5 years the difference in depreciation is 10,545.30 -6,332.78= $ 4,212.52 this is greater that the difference in the actual price 16,000-12,000 =$ 4,000
Jess should buy the Kia if wants to use the car for 10 years or more because Kia will depreciates less than Honda in 10 years.
In 10 years the difference in depreciation is 6,950.22 -3,342.01 =$ 3, 608.21 this is lower that the difference in the actual price 16,000-12,000 =$ 4,000
Cost of Honda car with 8% rate of depreciation after 5 and 10 year are 10,545 and 6950 respectively.
Cost of Kia car with the 12% rate of depreciation after 5 and 10 years are 6333 and 3342 respectively.
What is depreciation?
Depreciation refers to when the value of something goes down over time.
What is compound depreciation?
When an item of value $P depreciates at the rate of R% per year, the value $[tex]A_{n}[/tex] after n years is given by
[tex]An = P(1-R)^{n}[/tex]
According to the question
We have
Cost of Honda car is 16000
Rate of depreciation = 8% per annum
Cost of Kia car is 12000
Rate of depreciation = 12% per annum
Therefore,
Cost of Honda car after 5 years [tex]=16000(1-\frac{8}{100} )^{5} \\[/tex]= 10,545.3
And,
cost of Honda car after 10 years = [tex]16000(1-\frac{8}{100}) ^{10}[/tex] = 6950
Similarly,
Cost of Kia car after 5 years = [tex]12000(1-\frac{12}{100}) ^{5}[/tex]= 6,332.78
Cost of kia car after 10 years [tex]= 12000(1-\frac{12}{100}) ^{10} =3342[/tex]
Hence, Jess should buy Honda car because its rate of depreciation is less so in future if she wants to sell Honda car she will get profit.
Learn more about depreciation here:
https://brainly.com/question/15085226
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