Sum-of-years’-digits method is one of the the accelerated methods of depreciation and charges higher deprecation in earlier periods of useful life of asset and reduces with every passing period. This is achieved by applying a fraction that reduces every next period.

The numerator of fraction is asset’s remaining number of years of useful life whereas denominator is the sum of years of asset’s useful life. As time passes from one year to next, the numerator decreases however, denominator stays constant and result is decreasing fraction over the period of time which will be multiplied with depreciable value to compute depreciation of specific period.

Mathematically it can be expressed as follows:

SYD depreciation for the period = | Remaining useful life in years | x Cost – Expected residual value |

Sum of years of useful life |

If asset has really long useful life like 30 years or more then calculating sum of years’ digits then it becomes hectic. However, with the help of *triangular number formula *we can find the total easily. The formula is very simple:

= | n(n+1) |

2 |

where *n* is the total number of years.

**Example: Sum of Years’ Digits method Depreciation**

BnW frames bought a printing machine for $240,000. It is expected that machine has a useful life of 5 years at the end of which residual value will be $30,000. Entity uses sum-of-years’-digits method to calculate depreciation.

**Give a schedule showing depreciation of asset for 5 years with workings.**

Solution:

Year | Depreciable value (A) | Remaining Years | Fraction (B) | Formula (AxB) | Depreciation Expense |

1 | 210,000 | 5 | 5/15 | 210,000 x 5/15 | 70,000 |

2 | 210,000 | 4 | 4/15 | 210,000 x 4/15 | 56,000 |

3 | 210,000 | 3 | 3/15 | 210,000 x 3/15 | 42,000 |

4 | 210,000 | 2 | 2/15 | 210,000 x 2/15 | 28,000 |

5 | 210,000 | 1 | 1/15 | 210,000 x 1/15 | 14,000 |

Sum = 15 | 210,000 |