Nash Company purchases equipment on January 1, Year 1, at a cost of $480,000. The asset is expected to have a service life of 12 years and a salvage value of $43,200.

a. Compute the amount of depreciation for each of Years 1 through 3 using the straight-line depreciation.
b. Compute the amount of depreciation for each of Years 1 through 3 using the sum-of-the-years'-digits method.

Explanation:

The computation is shown below:

1. Under the straight line method

= (Purchase value of an equipment - salvage value) ÷ (service life)

= ($480,000 - $43,200) ÷ (12 years)

= ($436,800) ÷ (12 years)  

= $36,400

In this method, the depreciation is same for all the remaining useful life

So

Year 1 = $36,400

Year 2 = $36,400

Year 3 = $36,400

2. Under the sum of the years digit method

Depreciation factor is

= n × (n + 1) ÷ 2

= 12 × (12 + 1) ÷ 2

= 78

Now the depreciation expense is

Year 1

=  ($480,000 - $43,200)  × (12 years) ÷ (78 years)

= $67,200

Year 2

=  ($480,000 - $43,200)  × (11 years) ÷ (78 years)

= $61,600

Year 3

=  ($480,000 - $43,200)  × (10 years) ÷ (78 years)

= $56,000

looks

u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30