Use the sum-of-the-years'-digits method of depreciation. Round to the nearest dollar.
-Find the depreciation in the third year for a power generator which costs $25,000, has a life of 12
Years, and an estimated scrap value of $2,500.

Question

Quizplus · Accepted Answer

To use the sum-of-the-years'-digits method, we need to find the total number of years of useful life, which is calculated as follows:

1 + 2 + 3 + ... + 12 = 78

Next, we need to find the depreciation rate for each year of useful life. The rate for a particular year is calculated by dividing the number of years of useful life remaining at the beginning of that year by the sum of the years' digits:

Year 1: 12/78
Year 2: 11/78
Year 3: 10/78

And so on, until we get to:

Year 12: 1/78

To find the depreciation expense for each year, we multiply the depreciation rate by the depreciable cost (which is the original cost minus the estimated scrap value). In this case, the depreciable cost is:

$25,000 - $2,500 = $22,500

So the depreciation expense for each year is:

Year 1: (12/78) x $22,500 = $3,461
Year 2: (11/78) x $22,500 = $3,183
Year 3: (10/78) x $22,500 = $2,885

Rounding these answers to the nearest dollar, we get:

Year 1: $3,461
Year 2: $3,183
Year 3: $2,885

Therefore, the depreciation in the third year is $2,885, which corresponds to answer choice D. The depreciation expense using the sum-of-the-years'-digits method can be calculated as follows:

Step 1: Calculate the total number of digits in the sum-of-the-years' digits:
n = 1 + 2 + 3 + ... + 12 = 78

Step 2: Calculate the depreciation fraction for each year:
Year 1: 12/78
Year 2: 11/78
Year 3: 10/78

Step 3: Calculate the depreciation expense for each year:
Depreciation expense = (Cost - Scrap value) x Depreciation fraction

Year 1: (25,000 - 2,500) x 12/78 = $3,462
Year 2: (25,000 - 2,500) x 11/78 = $2,772
Year 3: (25,000 - 2,500) x 10/78 = $2,885

Therefore, the depreciation in the third year is $2,885, which is closest to option D, $2,885.

Use the Sum-Of-The-Years'-Digits Method of Depreciation