Sure, let's solve this step-by-step.
1. Determine the total amount depreciated over the life of the machine:
- The original cost of the machine is ₹ 1,00,000.
- The residual value of the machine at the end of its life is ₹ 2,000.
- The total amount depreciated over the machine's life is:
[tex]\[
\text{Total Depreciation} = \text{Original Cost} - \text{Residual Value}
\][/tex]
[tex]\[
\text{Total Depreciation} = ₹ 1,00,000 - ₹ 2,000 = ₹ 98,000
\][/tex]
2. Calculate the yearly depreciation:
- The machine's life is 5 years.
- Using the straight-line method (SLM), depreciation is spread evenly across each year.
- The yearly depreciation is:
[tex]\[
\text{Yearly Depreciation} = \frac{\text{Total Depreciation}}{\text{Life Years}}
\][/tex]
[tex]\[
\text{Yearly Depreciation} = \frac{₹ 98,000}{5} = ₹ 19,600
\][/tex]
3. Calculate the rate of depreciation per annum:
- The rate of depreciation per annum is determined by what percentage the yearly depreciation is of the original cost.
- The rate of depreciation is:
[tex]\[
\text{Rate of Depreciation} \ (\%) = \left(\frac{\text{Yearly Depreciation}}{\text{Original Cost}}\right) \times 100
\][/tex]
[tex]\[
\text{Rate of Depreciation} \ (\%) = \left(\frac{₹ 19,600}{₹ 1,00,000}\right) \times 100 = 19.6 \%
\][/tex]
So, the rate of depreciation per annum is [tex]\( \boxed{19.6\%} \)[/tex].
The correct answer from the given options is not listed here; the actual rate of depreciation per annum is [tex]\( 19.6\% \)[/tex].
