*total*amount of depreciation over an asset's useful life should be the same regardless of the depreciation method used. The difference is in the

*timing*of the total depreciation.

To illustrate the sum of the years' digits method of depreciation, let's assume that a plant asset is purchased at a cost of $160,000. The asset is expected to have a useful life of 5 years and then be sold for $10,000. This means that the asset's depreciable amount will be $150,000 to be expensed over its useful life of 5 years.

Next the digits in the years of the asset's useful life are summed: 1 + 2 + 3 + 4 + 5 = 15. In the first year of the asset's life, 5/15 of the depreciable amount (5/15 of $150,000) or $50,000 will be debited to Depreciation Expense and $50,000 will be credited to Accumulated Depreciation. In the second year of the asset's life, $40,000 (4/15 of $150,000) will be the depreciation amount. In the third year, $30,000 (3/15 of $150,000) will be the depreciation. The fourth year will be $20,000 (2/15 of $150,000) and the fifth year will be $10,000 (1/15 of $150,000). As indicated earlier, the

*total*

*depreciation during the asset's useful life needs to sum to the depreciable cost*(in this case $150,000) regardless of the depreciation method used.

Instead of adding the individual digits in the years of the asset's useful life, the following formula can be used: n(n+1) divided by 2. In this formula, n = the useful life in years. Let's use the formula to check our calculation above. When the useful life is 5 years, the formula will be 5(5+1)/2 = 5(6)/2 = 30/2 = 15. If the useful life is 10 years, the formula will show 10(10+1)/2 = 10(11)/2 = 110/2 = 55. In the first year of the asset having a 10 year useful life, the depreciation will be 10/55 of the asset's depreciable cost. The second year will be 9/55 of the asset's depreciable cost. In the tenth year, the depreciation will be 1/55 of the asset's depreciable cost.

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