# Sum of the years' digits

Sometimes organizations want to reflect what is called accelerated depreciation, or higher depreciation in earlier years and lower depreciation later over the span of an asset's useful life. There two methods for doing this, sum of the years' digits and double declining balance methods.

The first formula is:

`Annual depreciation expense = (Remaining Useful Life / ((Useful Life x (Useful Life + 1)) / 2)) x (Cost of the Asset - Salvage Value)`

The second formula is:

`Annual depreciation expense = (Remaining Useful Life / Sum of the Years) x (Cost of the Asset - Salvage Value)`

For example, formula 1, as hop purchases a machine for 50,000 Euros. The machine has an expected useful life of 3 years and the shop anticipates that it will be able to sell the machine for parts for 5,000 Euros at the end of its life.

The calculation for the first year of depreciation is:

```
= (3 Remaining Years / ((3 Years x (3 Years + 1)) / 2)) x (50,000 Euros - 5,000 Euros)
= (3 Remaining Years / ((3 Years x 4) / 2)) x 45,000 Euros
= (3 Remaining Years / (12/2)) x 45,000 Euros
= 3/6 x 45,000
= 22,500 Euros
```

The calculation for the second year of depreciation is:

```
= (2 Remaining Years / ((3 Years x (3 Years + 1)) / 2)) x (50,000 Euros - 5,000 Euros)
= (2 Remaining Years / ((3 Years x 4) / 2)) x 45,000 Euros
= (2 Remaining Years / (12/2)) x 45,000 Euros
= 2/6 x 45,000
= 15,000 Euros
```

The calculation for the third year of depreciation is:

```
= (1 Remaining Year / ((3 Years x (3 Years + 1)) / 2)) x (50,000 Euros - 5,000 Euros)
= (1 Remaining Year / (3 Years x 4) / 2)) x 45,000 Euros
= (1 Remaining Year / (12/2)) x 45,000 Euros
= 1/6 x 45,000
= 7,500 Euros
```

Using the same scenario with formula 2:

The calculation for the first year of depreciation is:

```
= (3 remaining years / (3 + 2 + 1)) x (50,000 Euros - 5,000 Euros)
= (3 remaining years / 6) x 45,000 Euros
= 22,500 Euros
```

The calculation for the second year of depreciation is:

```
= (2 remaining years / (3 + 2 + 1)) x (50,000 Euros - 5,000 Euros)
= (2 remaining years / 6) x 45,000 Euros
= 15,000 Euros
```

The calculation for the third year of depreciation is:

```
= (1 remaining year / (3 + 2 + 1)) x (50,000 Euros - 5,000 Euros)
= (1 remaining year / 6) x 45,000 Euros
= 7,500 Euros
```