In the SYD method of computing depreciation, what is the formula to compute the sum-of-years digits with n as the number of useful years of the equipment?

In the Sum-of-Years-Digits (SYD) method of computing depreciation, the formula for calculating the sum of the years' digits is essential for determining the annual depreciation expense for each period. The correct formula for the sum of years' digits involves the total number of useful years of the asset.

When calculating the sum for depreciation purposes, the formula is given by n(n + 1)/2, where n represents the total number of years of useful life of the asset. This formula derives from adding a sequence of integers from 1 to n, since each year of the asset's life contributes a different denominator for depreciation. The first year receives the most significant portion of the asset's value, while subsequent years receive progressively less, reflecting its decline in value more rapidly in the earlier years.

This method results in a declining depreciation amount each year, aligning well with the practical scenario of how assets typically lose value faster when they are new. Thus, this calculation provides a systematic way of capturing that depreciation impact over the asset's useful life.