# Sum of the Years' Digits Method of 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. The formula to calculate depreciation under SYD method is:

SYD Depreciation = | |

Depreciable Base × | Remaining Useful Life |

Sum of the Years' Digits |

In the above formula, depreciable base is the difference between cost and salvage value of the asset and sum of the years' digits 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 more conveniently using the following formula:

Sum of the Years' Digits = | n(n+1) |

2 |

Sum of the years' digits method can also be applied on monthly basis, in which case the above formula to calculate the sum of the years' digits 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