On this problem, I do not understand where the denominator of the sums of the years digits came from. Can someone explain the Sums of the years digits and the formula that is with it?

E20.16 Foster Company purchased a machine at a total cost of $220,000 (no residual value) at the beginning of 2015. The machine was being depreciated over a 10-year life using the sum-of-the-years'-digits method. At the beginning of 2018, it was decided to change to straight-line depreciation.

a. Will this change be accounted for using the retrospective or prospective approach?

The change will be prospective, because changes in depreciation methods, useful lives, and residual values are considered to be changes in estimates.

b. Ignoring taxes, the 2018 adjusting entry will include a debit to depreciation expense of:

1. $11,000
2. $16,000
3. $22,000
4. $38,000

Answer: b. Sum-of the years digits depreciation for 2015-2017 was $108,000 {$220,000 [(10 + 9+ 8) / 55]}. Thus, the undepreciated value at the beginning of 2018 is $112,000 ($220,000 $108,000), which will be depreciated over seven years. $112,000 / 7 years = $16,000.