If an asset has a 10-year estimated life, what number should be used as the numerator for the SYD method at the end of Year 1?

In the Sum of the Years' Digits (SYD) method of depreciation, the denominator is the sum of the digits representing the total useful life of an asset. For an asset with a 10-year estimated life, the sum of the digits from 1 to 10 is calculated as follows:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.

For the numerator used in the depreciation calculation for Year 1, you start with the total estimated life (which is 10 years) and subtract the number of years already utilized at the end of Year 1. Since Year 1 is complete, you need to consider the remaining life at the end of this year, which is 10 - 1 = 9.

In the SYD formula, the numerator for the first year is derived from the total life remaining aspect. Thus, the appropriate number to use at the end of Year 1 is indeed 10, representing the full initial life of the asset at Year 1 before any depreciation is taken.

Therefore, using the full remaining time gives justification for years accounted for in future depreciation calculations, leading to the