# Sum of Years of Digit Method

This method is in the pattern of diminishing balance method. The amount of depreciation to be charged to the Profit and Loss account under this method goes on decreasing. The steps involved in the working of this method are given below:

**Step 1:** Calculate the â€˜sum of yearsâ€™ as under:

where â€˜nâ€™= useful life of the asset

**Step 2: **Calculate the rate of depreciation for various years up to the useful life as under

For first year = (nth year / Sum of years digit) x100 = _____%

For second year = [ (n-1)th year / Sum of years digit] x 100 = _____%

For third year = [(n-2)th year / Sum of years digit ] x 100 = _____%

For nth year = (1/ Sum of years digit) x 100 = _____%

**Step 3:** Calculate the amount of depreciation as under:

Amount of depreciation = (Original cost less estimated scrap value) x Respective rate of depreciation for the given year

**Note: **This method is not yet in vogue in India its advantages are the same as those of reducing balance method.

**Illustration 6**

On 1st April 2011, A Ltd. purchased machinery for â‚¹ 50,000 and incurred â‚¹ 3,500 towards freight and insurance, â‚¹ 500 towards carriage inwards and â‚¹ 1,000 towards installation charges. It was established that the machinery will have a scrap value of â‚¹ 5,000 at the end of its useful life, which is 4 years. On 1st April, 2014, â‚¹ 1,000 was spent on repairs and renewals of the machine.

You are required to

- Calculate the amount of Depreciation
- Calculate the rate of Depreciation
- Show the Machinery Account for the first four financial years ending on 31st March each year according to the Sum of Yearâ€™s Digits Method.

**Solution:**

Sum of Yearâ€™s Digits = n (n + 1)/2 = 4(4 + 1)/2 = 10

**Rate of Depreciation** =

1st Year = 4/10 x 100 = 40%

2nd Year = 3/10 x 100 = 30%

3rd Year = 2/10 x 100 = 20%

4th Year = 1/10 x 100 = 10%

**Calculation of the Amount of Depreciation p.a.**