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A car is valued at $35400 at the start of the year, and at $25700 at the end of that year. During that year, the car travelled 25000kms.
a) Find the total depreciation of the car in that year in dollars
b) Find the depreciation per kilometre for this car
c) Using (initial value) -> V₀ = 35400, write down a rule for the value of the car Vₙ after ₙ kilometres
d) How many kilometres are travelled when the value of the car is $6688?
e) Including the first year of travel, how many kilometres in total is this car expected to drive before it has a value of 0?

Respuesta :

a. Total depreciation = $9700

b. Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = $35400 +  ₙt

d. Distance = 4723. 16 kilometers

e. Total distance =  29723. 16 kilometers.

How to determine the depreciation

i. The formula for total depreciation is given as;

Total depreciation = Cost of asset - Residual value

Cost of car = $ 35400

Residual value = $25700

Total depreciation = $35400 - $25700

Total depreciation = $9700

b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers

Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]

Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = V₀ + ₙt

t = time of depreciation

V₀ = $35400

Vₙ = $35400 +  ₙt

d. When the car costs $35400, it travelled 25000 kilometers

It costs $6688, it would travel 'x' kilometers

Cross multiply

$35400 × x = $ 6688 × 25000 kilometers

Make 'x' subject

x = [tex]\frac{6688 * 25000}{35400}[/tex]

x = [tex]\frac{167200000}{35400}[/tex]

x = [tex]4723. 16[/tex] kilometers

The car would travel 4723. 16 kilometers

e. To find the total distance

Total distance = 25000 + 4723. 16

Total distance =  29723. 16 kilometers.

Learn more about depreciation here:

https://brainly.com/question/25297296

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