Question

Spencer estimates that his new car that costs $24,380 would be worth $13, 500 after two years and $8,230 after five years. a.) What will be the annual rate of depreciation for the first two years? b.) What will the percent be for the five years?

Answer 1

22.31%, 13.25%

Explanation:

Given:

Spencer estimates that his new car that costs $24,380 would be worth $13, 500 after two years

And would be worth $8,230 after five years.

Question asked:

What will be the annual rate of depreciation for the first two years ?

What will the percent be for the five years ?

Solution:

Cost of asset (new car) = $24,380

Scrap value of the car after two years = $13, 500

We have to find rate of depreciation for first two years.

So, useful life will be = 2 years

First of all we will find annual depreciation, then rate of depreciation.

`Annual\ Depreciation = ((Cost\ of\ Asset\ - Net\ Scrap\ Value))/(Useful\ Life)`

`=(24380-13500)/(2) \\ \\ =(10880)/(2) \\ \\ =5440`

Annual depreciation = 5440

Now,

`Rate\ of \ depreciation = (Annual\ Depreciation)/(Cost\ of\ Asset)*100`

`=(5440)/(24380)*100=(544000)/(24380) =22.31\%`

Therefore, annual rate of depreciation for the first two years is 22.31%.

Similarly, we will find rate of depreciation for 5 years.

This time useful life, we will consider 5 years:

Scrap value = $8,230 after five years (given)

`Annual\ Depreciation = ((Cost\ of\ Asset\ - Net\ Scrap\ Value))/(Useful\ Life)`

`=(24380-8230)/(5) \\ \\ =(16150)/(5) \\ \\ =3230`

Annual depreciation = 3230

`Rate\ of \ depreciation = (Annual\ Depreciation)/(Cost\ of\ Asset)*100`

`=(3230)/(24380) *100\\ \\ =13.25\%`

Therefore, annual rate of depreciation for the five years is 13.25%