# Sum of the Years’ Digits Depreciation

Sum of the years’ digits method of depreciation is one of the accelerated depreciation techniques which are based on the assumption that assets are generally more productive when they are new and their productivity decreases as they become old.

## Formula

The formula to calculate depreciation under SYD method is:

$$ SYD\ Depreciation \\= Depreciable\ Base × \frac{Remaining\ Life}{SYD} $$

In the above formula, depreciable base is the difference between cost and salvage value of the asset and SYD is the sum of the series:

*1, 2, 3, ... , n* ; where *n* is the useful life of the asset in years.

Sum of the years’ digits can be calculated conveniently using the following formula:

$$ Sum\ of\ the\ Years’\ Digits = \frac{n(n+1)}{2} $$

SYD method can also be applied on monthly basis, in which case the above formula to calculate the sum of a series becomes much useful.

## Example

Use sum of the years' digits method of depreciation to prepare a depreciation schedule of the following asset:

Cost | $45,000 |

Salvage Value | $5,000 |

Useful Life in Years | 4 |

Asset is Depreciated | Yearly |

__Solution__

Sum of the Years' Digits = 1 + 2 + 3 + 4 = 4(4 + 1) ÷ 2 = 10

Depreciable Base = $45,000 − $5,000 = $40,000

Year | Depreciable Base | Depreciation Factor | Depreciation Expense | Accumulated Depreciation | |

1 | $40,000 | 4/10 | 4/10 × 40,000 = | 16,000 | $16,000 |

2 | $40,000 | 3/10 | 3/10 × 40,000 = | 12,000 | $28,000 |

3 | $40,000 | 2/10 | 2/10 × 40,000 = | 8,000 | $36,000 |

4 | $40,000 | 1/10 | 1/10 × 40,000 = | 4,000 | $40,000 |

Written by Irfanullah Jan and last revised on