Mathematics for FinanceMTP June 24 Series IQuestion 1408 of 512
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The Scrap value of machine valued at Rs.10,00,000\displaystyle 10,00,000 after 15 years of depreciation is 10%\displaystyle 10\% p.a.

Options

A215891.13\displaystyle 215891.13
B205891.13\displaystyle 205891.13
C225891.13\displaystyle 225891.13
DNone
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Correct Answer

✅ Option b — 205891.13\displaystyle 205891.13

All Options:

  • A215891.13\displaystyle 215891.13
  • B205891.13\displaystyle 205891.13
  • C225891.13\displaystyle 225891.13
  • DNone

Detailed Solution & Explanation

Given parameters: * Initial Value of the machine (C\displaystyle C) = Rs. 10,00,000\displaystyle \text{Rs. }10,00,000 * Rate of depreciation (d\displaystyle d) = 10%\displaystyle 10\% p.a. =0.10\displaystyle = 0.10 * Time (n\displaystyle n) = 15\displaystyle 15 years The Scrap Value (SV\displaystyle SV) after depreciation is given by the formula: SV=C(1−d)nSV = C(1 - d)^n Substituting the values: SV=10,00,000×(1−0.10)15SV = 10,00,000 \times (1 - 0.10)^{15} SV=10,00,000×(0.9)15SV = 10,00,000 \times (0.9)^{15} First, let's calculate (0.9)15\displaystyle (0.9)^{15}: (0.9)15≈0.205891132(0.9)^{15} \approx 0.205891132 Now substitute this back: SV=10,00,000×0.205891132=2,05,891.13SV = 10,00,000 \times 0.205891132 = 2,05,891.13 Thus, the scrap value is approximately Rs. 2,05,891.13\displaystyle \text{Rs. }2,05,891.13. Hence, **Option B** is the correct answer.

Key Concepts to Understand

Depreciation

Allocation of the cost of a tangible fixed asset over its useful life due to wear and tear, efflux of time, or obsolescence.

More Questions from Mathematics for Finance

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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