GATE 2022 CH – Question 35
A compressor with a life of 10 years costs Rs 10 lakhs. Its yearly operating cost is Rs 0.5 lakh. If the annual compound interest rate is 8%, the amount needed at present to fund perpetual operation of the compressor is Rs _________ lakhs (rounded to first decimal place).
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Correct answer: 24.78 to 25.02
Explanation
The capitalised cost is $C_K = C + \frac{C}{(1 + i)^n - 1} + \frac{\text{operating cost}}{i} = 10 + \frac{10}{1.08^{10} - 1} + \frac{0.5}{0.08} = 10 + 8.629 + 6.25 = 24.9$ lakhs.