Q.An asset costing ₹10,000 is expected to have a useful life of 4 years and a scrap value of zero. Find the annual depreciation charge using the sum-of-the-years digits method.

The key idea here is Sum-of-the-Years’ Digits (SYD) depreciation, which accelerates depreciation compared to the straight-line method.

Step 1: Compute the sum of the years’ digits.

For a 4-year life:

$1 + 2 + 3 + 4 = 10$

Step 2: The depreciable amount is cost minus scrap value:

$10,000 - 0 = ₹10,000$

Step 3: The annual depreciation for year $n$ is:

$\frac{\text{Remaining life at start of year}}{\text{Sum of years}} \times \text{Depreciable amount}$

For Year 1: $\frac{4}{10} \times 10,000 = ₹4,000$ …

The sum-of-the-years' digits method is an accelerated depreciation technique. Unlike straight-line depreciation, which spreads the cost evenly, this method allocates a larger portion of the asset's cost to the earlier years of its useful life. The logic is that many assets lose more value in their first few years of use — think of a new car's steep initial depreciation.

The method works by creating a fraction for each year. The denominator of this fraction is the sum of the digits of the asset's useful life. For a 4-year life, that sum is $1 + 2 + 3 + 4 = 10$. The numerator for each year is the remaining useful life at the start of that year. So in year 1, the fraction is $\frac{4}{10}$; in year 2, $\frac{3}{10}$; in year 3, $\frac{2}{10}$; and in year 4, $\frac{1}{10}$.

You multiply each year's fraction by the depreciable amount — which is the original cost minus the scrap value. Here, scrap value is zero, so the depreciable amount is simply ₹10,000.

Let's work through each year:

1. Year 1: Remaining life at start = 4 years. Fraction = $\frac{4}{10}$. Depreciation charge = $\frac{4}{10} \times 10,000 = 4,000$.
2. Year 2: Remaining life at start = 3 years. Fraction = $\frac{3}{10}$. Depreciation charge = $\frac{3}{10} \times 10,000 = 3,000$.
3. Year 3: Remaining life at start = 2 years. Fraction = $\frac{2}{10}$. Depreciation charge = $\frac{2}{10} \times 10,000 = 2,000$.
4. Year 4: Remaining life at start = 1 year. Fraction = $\frac{1}{10}$. Depreciation charge = $\frac{1}{10} \times 10,000 = 1,000$.

Notice that the charges decrease by a constant amount each year — here, by ₹1,000. That's a neat property of this method when scrap value is zero. …