Sum of years digits depreciation, explained and calculated

In short

Sum of years digits is an accelerated method that weights each year by its position in the remaining life, so earlier years take a larger share of the depreciable amount. Cohiva Control computes it natively with fixed-precision decimal arithmetic rounded half up, holds a residual-value floor, and posts the monthly journal to Xero, QuickBooks, NetSuite or Crunch.

Worked example: Sum of Years' Digits monthly schedule

Asset cost: $42,000.00Residual value: $2,000.00Useful life: 60 months (5 years)

Month	Opening book value	Depreciation	Closing book value
1	$42000.00	$1111.11	$40888.89
2	$40888.89	$1092.59	$39796.30
3	$39796.30	$1074.07	$38722.22
4	$38722.22	$1055.56	$37666.67
5	$37666.67	$1037.04	$36629.63
6	$36629.63	$1018.52	$35611.11
7	$35611.11	$1000.00	$34611.11
8	$34611.11	$981.48	$33629.63
9	$33629.63	$962.96	$32666.67
10	$32666.67	$944.44	$31722.22
11	$31722.22	$925.93	$30796.30
12	$30796.30	$907.41	$29888.89

Figures are computed by the same depreciation engine Cohiva Control uses in the product (money as NUMERIC(19,4), rounded ROUND_HALF_UP), shown for the first 12 months of an illustrative asset.

Sum of years digits depreciation, explained and calculated

Sum of years digits is an accelerated method with a gentler shape than the declining-balance family. Rather than applying a rate to a shrinking book value, it splits the fixed depreciable amount into fractions that decline year on year, so the early years carry more and the taper is smooth and predictable. This page explains the method, walks through a worked example, and shows how Cohiva Control computes it.

How sum of years digits works

First, add up the digits of the years in the asset’s life. For a five-year asset that is 5 plus 4 plus 3 plus 2 plus 1, which equals 15. The general form is n times (n plus 1) divided by 2. Then each year takes a fraction of the depreciable amount equal to its remaining years over that sum:

Year one takes 5 fifteenths, year two takes 4 fifteenths, and so on down to 1 fifteenth in the final year.
The annual charge applies that fraction to the depreciable amount; the monthly charge is one twelfth of the annual figure.

Because the fractions add up to one, the total charge over the life equals the depreciable amount exactly.

A worked example

The calculator above uses a cost of 42,000, a residual value of 2,000 and a 60-month, five-year life, so the depreciable amount is 40,000 and the sum of the years’ digits is 15. Year one’s fraction is 5 fifteenths of 40,000, which is 13,333.33 a year, or 1,111.11 a month. That is what the first month charges, leaving a book value of 40,888.89. The monthly charge then steps down through the year and again at each year boundary as the fraction falls. The figures come from the product’s depreciation engine, so they match what Cohiva Control posts.

When to use it

Sum of years digits suits assets where you want acceleration but prefer a smooth, predictable decline to the sharper curve of diminishing value or double declining balance. The charge is easy to forecast because it follows a fixed schedule of fractions rather than a book-value-driven rate. If you want even charges, straight-line is simpler; if you want the steepest front-load, double declining balance goes further.

How Cohiva Control computes it

Cohiva Control builds the fraction for the period from the asset’s remaining life and applies it to the depreciable amount through the same engine the product uses internally. Money is a fixed-precision decimal rounded half up, never a floating point number, and the residual-value floor ensures the asset never depreciates below residual.

Each monthly run writes to an append-only depreciation ledger and can post a journal to Xero, QuickBooks, NetSuite or Cohiva Crunch. The run is idempotent, posting state is tracked separately from the immutable ledger row, and the asset you depreciate is the same asset your team maintains.

Part of the Cohiva platform

Cohiva Control is part of the Cohiva platform. Leisure operators often run it with Cohiva Complex, and finance teams connect it to Cohiva Crunch for the general ledger. Explore the platform at www.cohiva.app.

This page provides general information about how Cohiva Control calculates depreciation. It is not accounting, tax or financial advice. Confirm treatment with your accountant or adviser.

Frequently asked questions

What is the sum of years digits formula?

The annual fraction equals remaining years divided by the sum of the years' digits, where the sum is n times (n plus 1) divided by 2. The annual charge applies that fraction to the depreciable amount, and the monthly charge is one twelfth of it.

How is it different from declining balance methods?

Declining balance methods apply a rate to the reducing book value. Sum of years digits applies a fraction to the fixed depreciable amount, giving a smooth, predictable taper rather than a curve driven by book value.

When should I use it?

Use it when you want accelerated depreciation with a steady, predictable taper rather than the sharper curve of diminishing value or double declining balance.

Does it land at residual cleanly?

Yes. Because the fractions across the life sum to one, the total charge equals the depreciable amount, and the residual-value floor protects against rounding taking the asset below residual.

Where do the journals go?

Each monthly run writes to an append-only depreciation ledger and can post a journal to Xero, QuickBooks, NetSuite or Cohiva Crunch, idempotently.