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

Answer:

22.31%, 13.25%

Step-by-step 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.

$Annual\ Depreciation = \frac{(Cost\ of\ Asset\ - Net\ Scrap\ Value)}{Useful\ Life}$

                                  $=\frac{24380-13500}{2} \\ \\ =\frac{10880}{2} \\ \\ =5440$

Annual depreciation = 5440

Now,

$Rate\ of \ depreciation = \frac{Annual\ Depreciation}{Cost\ of\ Asset}\times100$

                                  $=\frac{5440}{24380}\times100=\frac{544000}{24380} =22.31\%$

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)

$Annual\ Depreciation = \frac{(Cost\ of\ Asset\ - Net\ Scrap\ Value)}{Useful\ Life}$

                                   $=\frac{24380-8230}{5} \\ \\ =\frac{16150}{5} \\ \\ =3230$

Annual depreciation = 3230

$Rate\ of \ depreciation = \frac{Annual\ Depreciation}{Cost\ of\ Asset}\times100$

                                  $=\frac{3230}{24380} \times100\\ \\ =13.25\%$

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