GATE 2023 CH – Question 64
The purchase cost of a new distillation column is Rs. 10 lakhs with an installation factor of 5.8. The cost of the capital is to be annualized over a period of 6 years at a fixed rate of interest of 5% per annum, compounded annually. The annual cost (in lakhs of rupees) of the installed capital is _______ (rounded off to one decimal place).
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Correct answer: 11.34 to 11.46
Explanation
The installed cost is $10 \times 5.8 = 58$ lakhs. The capital recovery factor is $\frac{i(1 + i)^n}{(1 + i)^n - 1} = \frac{0.05 \times 1.3401}{0.3401} = 0.19702$. The annual cost is $58 \times 0.19702 = 11.43$ lakhs, about 11.4.