Sum of the years digits depreciation

Definition: A method of depreciation, used by companies to compute their income tax liabilities, that provides for greater depreciation in earlier years of a piece of equipment’s life than the straight-line method.

Example: A company buys an industrial washing machine for $3,000 to wash the uniforms that it rents out to clients. The useful life of the machines is four years. At that time, the machine will have no salvage value

We have to come up with a way to weigh the earlier years more heavily. First, we’ll add up each of the years in over the useful life of the asset: 1+2+3+4=10. We’ll use that as our denominator. Next, we’ll calculate each year’s depreciation as follows:

Year 1 depreciation = 4 / 10 * $3,000, or $1,200

Year 2 depreciation = 3 / 10 * $3,000, or $   900

Year 3 depreciation = 2 / 10 * $3,000, or $   600

Year 4 depreciation = 1 / 10 * $3,000, or $   300

Investeach explains: Although it’s not immediately apparent, accelerated depreciation allows companies to lower their income taxes. See Accelerated depreciation for an explanation.

Riddle me this:

1. What would have been the depreciation recorded for this machine under straight-line depreciation?
2. What benefit does accelerated depreciation provide companies?
3. Why, by adding up the years digits and using the total as the denominator, do we ensure that we will record the full depreciation over the asset’s useful life?