Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 9

Overview

A machine is purchased for Rs.20,000. Depreciates at 6% per annum for the first four years and after that 8% per annum for the next six years. Depreciation being calculated on diminishing value. Find the value of the machine after a period of 10 years.

Initial value ( V_0 = 20000 ).

After first 4 years at 6%: [ V_4 = 20000 \times (0.94)^4. ] [ (0.94)^2 = 0.8836,\quad (0.94)^4 = 0.78074896, ] [ V_4 = 20000 \times 0.78074896 = 15614.9792. ]

Next 6 years at 8%: [ V_{10} = V_4 \times (0.92)^6. ] [ (0.92)^2 = 0.8464,\quad (0.92)^4 = 0.71639296,\quad (0.92)^6 = 0.71639296\times 0.8464 \approx 0.606355. ] [ V_{10} \approx 15614.9792 \times 0.606355 \approx 9467.3. ]

Answer: Rs. 9467.30 (approx.)

Discuss theoretical concepts, mathematical formulas, and architectural foundations.

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