GATE 2025 CH – Question 63
It is proposed to install thermal insulation in a residence to save on the summer-monsoon season air-conditioning costs. The estimated yearly saving is 20 thousand rupees. The cost of installation of the insulation is 150 thousand rupees. The life of the insulation is 12 years. For a compound interest rate of 9% per annum, the minimum salvage value of the insulation for which the proposal is competitive, is ____ thousand rupees (rounded off to nearest integer).
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Correct answer: 19
Explanation
The proposal is competitive when the present worth of the savings and of the salvage value at least equals the installation cost. The present worth of 12 yearly savings of 20 at 9 % is $20 \times \frac{1 - 1.09^{-12}}{0.09} = 20 \times 7.1607 = 143.21$. The shortfall is $150 - 143.21 = 6.79$, which must come from the salvage value $S$ received in year 12: $S \times 1.09^{-12} = 6.79$, so $S = 6.79 \times 2.8127 = 19.1$, which is about 19 thousand rupees.