Declining fractions of the depreciable base
Sum-of-years’-digits is an accelerated US book method between straight-line and double-declining balance. The denominator is n(n + 1)/2. Year t multiplies cost minus salvage by remaining life ÷ that sum. Straight-line spreads the same base evenly. Double-declining balance applies 2 ÷ years to beginning book value and may leave a residual when salvage is $0. This page matches Excel SYD and does not load MACRS tables.
Year t expense = (cost − salvage) × (years − t + 1) ÷ SYD
Book value = cost − accumulated depreciation
Example
A $10,000 machine with $1,000 salvage and a 5-year life has SYD 15 and a $9,000 depreciable base. Year 1 is 5/15 × $9,000 = $3,000. Year 2 is $2,400. Year 5 is $600, and book value equals salvage. Excel’s $30,000 / $7,500 / 10-year example is $4,090.91 in year 1.
What this schedule leaves out
Useful life and the year to report must be whole numbers. Year 0 leaves book value equal to cost. Partial-year conventions, Section 179, and IRS MACRS percentages stay outside this full-year identity. The fractions add to 1, so the last year reaches salvage without a switch to straight-line.