### 4.4 Depreciation

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• Math Help

Note that the numerator (the top number) in the depreciation rate

is the number of years of useful life remaining at the beginning of the year. For instance, in Example 5, the useful life is 5 years. So, at the beginning of the first year, there are 5 years of useful life remaining and the numerator of the fraction is 5. At the beginning of the second year, there are 4 years of useful life remaining and the numerator of the fraction is 4, and so on.

In Example 5, be sure you understand that the depreciation in Column C (of the spreadsheet) is found by multiplying the deprecation rate by the difference between the purchase price and the salvage value. Because the difference between the purchase price and the salvage value is

you can calculate the depreciation for each year as shown.

In general, the depreciation in year k for the sum of the years-digits method is

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• Checkpoint Solution

Find the depreciation rate for year k when the useful life, n, is 4 years.

So, the amount of depreciation in year k is

A spreadsheet showing the sum of the years-digits depreciation schedule is shown below.

You can check your work using a depreciation schedule calculator located in Tools.

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