Using the sum-of-the years'-digits method,depreciation for 2017 and book value at December 31,2017,would be
A)$13,500 and $13,500.
B)$13,500 and $8,500.
C)$12,000 and $17,000.
D)$12,000 and $12,000.

Question

Quizplus · Accepted Answer

To calculate depreciation using the sum-of-the-years'-digits method, follow these steps:
1. Determine the useful life of the asset in years (in this case, 5 years).
2. Add the digits of the useful life together (5 + 4 + 3 + 2 + 1 = 15).
3. For each year, calculate the fraction of the total digits that the year represents. For example, in year 1, the fraction would be 5/15, in year 2 it would be 4/15, and so on.
4. Multiply the cost of the asset by the fraction for each year to get the depreciation expense for that year.

In this problem, the asset cost $67,500 and has a useful life of 5 years. Therefore, the total digits are 15. The fractions for each year are as follows:

Year 1: 5/15
Year 2: 4/15
Year 3: 3/15
Year 4: 2/15
Year 5: 1/15

Using these fractions, we can calculate the depreciation expense for each year:

Year 1: (5/15) x $67,500 = $22,500
Year 2: (4/15) x $67,500 = $18,000
Year 3: (3/15) x $67,500 = $13,500
Year 4: (2/15) x $67,500 = $9,000
Year 5: (1/15) x $67,500 = $4,500

Therefore, depreciation for 2017 (year 3) would be $13,500. To calculate book value at December 31, 2017, we subtract accumulated depreciation ($22,500 + $18,000 + $13,500 = $54,000) from the cost of the asset:

$67,500 - $54,000 = $13,500

So the book value at December 31, 2017, would also be $13,500. Therefore, the best choice is C.

Using the Sum-Of-The Years'-Digits Method,depreciation for 2017 and Book Value