A piece of equipment cost a certain factory Rs.600,000. Ifit depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

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Solution

Depreciation after 1st year =600,000 × (15/100) = Rs 90,000
Depreciation after 2nd year =600,000 × (13.5/100) = Rs 81,000
Depreciation after 10th year =600,000 × 1.5/100 = Rs 9,000
Total depreciation = 90000 + 81000 + 72000+ …+ 9000
Here a = 90000, d = 81000 – 90000 = – 9000, t₁₀ = 9000
Sum of n terms of AP is

$S_{n} = \frac{n}{2} (a + l)$
$S_{10} = \frac{10}{2} (90000 + 90000)$
= 5 × 99000 = 495000
Value at the end of 10 years = Rs 600000 – Rs 495000 = Rs. 1,05,000

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