# Sum of the Years Digits Depreciation

The sum of the years digits depreciation method (SYD depreciation) is used to calculate the annual depreciation expense of a fixed asset.

The purpose of using the sum of the years digits depreciation method is to produce a depreciation expense which is higher in the earlier years than in the later years of the assets useful life, as such it can be classified as an accelerated depreciation method.

The method takes the total depreciation over the useful life of the asset and allocates this to each year in proportion to the remaining life of the asset at the beginning of the year.

## Sum of the Years Digits Depreciation Formula

The depreciation charge for a particular year is given by the sum of the years digits depreciation formula as follows:

SYD depreciation = Total depreciation x Remaining life / SYD useful life

Where:
Total depreciation is the cost of the asset less the salvage value.
Remaining life is the useful life remaining at the beginning of the year.
SYD useful life is the sum of the years digits for the useful life

Since the remaining life is declining each year, the depreciation charge will decline each year.

## Calculation of SYD

The sum of years digits (SYD) is simply the sum of the year numbers. So for example, if there are 3 years then the sum of years digits is equal to 1+2+3 = 6, if there are 8 years then the SYD is equal to 1+2+3+4+5+6+7+8 = 36. This process can be summarized in the sum of years digits formula as follows:

Sum of the years digits = n x (n + 1) / 2

Where:
n is the number of years.

For example if there are 8 years as above,

```Useful life  = 8 years
SYD = n x (n + 1) / 2
SYD = 8 x (8 + 1) / 2
SYD = 36
```

## Sum of the Years Digits Depreciation Example

Suppose a business purchases an asset costing 9,000 with an estimated salvage value of 1,000 after a useful life of 4 years.

### Step 1: Calculate SYD

The first step is to calculate the sum of the years digits (SYD) for the useful life of the asset using the sum of years digits formula.

```Useful life  = 4 years
SYD useful life = n x (n + 1) / 2
SYD useful life = 4 x (4 + 1) / 2
SYD useful life = 10
```

### Step 2: Calculate Total Depreciation

The next step is to calculate the total depreciation required over the lifetime of the asset, which is simply the cost of the asset less its salvage value.

```Cost = 9,000
Salvage value = 1,000
Total depreciation = Cost - Salvage value
Total depreciation = 9,000 - 1,000
Total depreciation = 8,000
```

### Step 3: Allocate Depreciation to Years

The final step is to allocate this total depreciation to each of the years of its useful life in proportion to the remaining life of the asset at the beginning of the year using the sum of the years digits depreciation formula.

```Total depreciation = 8,000
SYD useful life = 10

Year 1
Remaining life at start of the year = 4

Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life
Sum of the years digits depreciation = 8,000 x 4 / 10
Sum of the years digits depreciation = 3,200

Year 2
Remaining life at start of the year = 3

Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life
Sum of the years digits depreciation = 8,000 x 3 / 10
Sum of the years digits depreciation = 2,400

Year 3
Remaining life at start of the year = 2

Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life
Sum of the years digits depreciation = 8,000 x 2 / 10
Sum of the years digits depreciation = 1,600

Year 4
Remaining life at start of the year = 1

Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life
Sum of the years digits depreciation = 8,000 x 1 / 10
Sum of the years digits depreciation = 800
```

The table below summarizes the breakdown of the depreciation expenses for each year. Notice that the depreciation is highest in the first year and is declining each year which means that the sum of the years digits depreciation is an accelerated depreciation method. In addition the total depreciation is 8,000 which is the same as the cost less the salvage value of the asset.

Our sum of years digits depreciation calculator is available and can be used to calculate the depreciation expense by entering details relating to the cost of the asset, the asset salvage value at the end of its useful life, and the number of periods in the useful lifetime.