a company purchased a lathe with a useful life of 4 years and a salavage value of $5,000.00 if the lathe cost $45,000.00 what is the lathes first year depreciation using the sum-of-the years digits method?

would it be $12,000.00

To calculate the lathe's first-year depreciation using the sum-of-the-years-digits method, you need to follow these steps:

Step 1: Calculate the sum of the digits
The sum of the digits can be calculated by using the formula n(n+1)/2, where n is the useful life of the asset. In this case, the useful life of the lathe is 4 years, so the sum of the digits is (4 * (4+1))/2 = 10.

Step 2: Calculate the depreciation expense for each year
To determine the depreciation expense for each year, you divide the remaining useful life by the sum of the digits. The formula is (remaining useful life / sum of the digits) * (initial cost - salvage value).

In the first year, the remaining useful life is 4 years, so the calculation would be:
(4 / 10) * ($45,000 - $5,000) = (0.4) * ($40,000) = $16,000.

Therefore, the lathe's first-year depreciation using the sum-of-the-years-digits method would be $16,000, not $12,000.