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# Sum of the Years' Digits Method of Depreciation:

## Definition and Explanation:

This method is introduced by American accountants. It is an improvement over diminishing balance method of depreciation. Here also the depreciation charge constantly reduces. This method is normally applied to fairly long lived assets. Unlike the diminishing balance method, a constantly decreasing rate is applied on the original cost. Hence the original book value is, like straight line method, reducible to zero. The determination of rate of depreciation is very simple. It simply sums up the years in an asset's lifespan to be used as denominator, and reverses the individual year numbers to be used as numerator.

## Example:

Suppose the cost, residual value and life of the asset are :

 Cost \$75,000 Residual value \$3,000 Life of the asset 8 Years

The denominator will be:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

The numerators from first to 8th year will respectively be 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1. Applying the rate to the depreciable cost 'original cost - residual value' i.e., \$72,000, the depreciation charges for the first eight years will be:

 Year Opening book value Depreciable cost Rate Depreciation Total depreciation Written down value 1 75,000 72,000 8/36 16,000 16,000 59,000 2 59,000 72,000 7/36 14,000 30,000 45,000 3 45,000 72,000 6/36 12,000 42,000 33,000 4 33,000 72,000 5/36 10,000 52,000 23,000 5 23,000 72,000 4/36 8,000 60,000 15,000 6 15,000 72,000 3/36 6,000 66,000 9,000 7 9,000 72,000 2/36 4,000 70,000 5,000 8 5,000 72,000 1/36 2,000 72,000 3,000

## Formula:

Sum of year's digits can be easily computed by the following formula:

 S = n (n + 1)/2 Where: S = Sum of years n = number of years of useful life of assets. Applying it when n = 8 years. S = 8 (8 + 1)/2 = 72/2 or 36

## More study material from this topic: Definition, explanation and causes of depreciation Depreciation is not a matter of valuation but a means of cost allocation Activity method of depreciation Straight line method of depreciation Sum of the years' digits method of depreciation Reducing balance method Annuity method Depreciation fund method or sinking fund method Insurance policy method Revaluation method Depletion method Machine hour rate, mileage, and global method Methods of recording depreciation Reserves Difference between general reserve and specific reserve Difference between capital reserve and general reserve Difference between reserve and reserve fund Difference between provision and reserve

A D V E R T I S E M E N T

 Financial Accounting Topics Introduction to Accounting ---------------------------------------------------------------------------- Transactions and Accounting Equation ---------------------------------------------------------------------------- Analysis of Business Transactions ---------------------------------------------------------------------------- Journal, Ledger and Trial Balance ---------------------------------------------------------------------------- Accounting for Bills of Exchange ---------------------------------------------------------------------------- Special Journals ---------------------------------------------------------------------------- Cash Book ---------------------------------------------------------------------------- Bank Reconciliation Statement ---------------------------------------------------------------------------- Final Accounts ---------------------------------------------------------------------------- Work Sheet ---------------------------------------------------------------------------- Capital and Revenue Items ---------------------------------------------------------------------------- Valuation of Inventories ---------------------------------------------------------------------------- Accounts of Non-profit Making Organizations ---------------------------------------------------------------------------- Statement of Cash Flows ---------------------------------------------------------------------------- Accounting Ratios Analysis ---------------------------------------------------------------------------- Depreciation, Provisions and Reserves ---------------------------------------------------------------------------- Accounting Dictionary ---------------------------------------------------------------------------- Financial Calculators

 Managerial Accounting Topics Financial Statements ---------------------------------------------------------------------------- Cost Volume Profit Relationship ---------------------------------------------------------------------------- Variable Costing System ---------------------------------------------------------------------------- Materials and Inventory Cost Control ---------------------------------------------------------------------------- Activity Based Costing System ---------------------------------------------------------------------------- Standard Costing and Variance Analysis ---------------------------------------------------------------------------- Balanced Scorecard ---------------------------------------------------------------------------- Capital Investment Analysis/Capital Budgeting  