Mathematics of FinanceMCQMTP 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 b205891.13\displaystyle 205891.13

All Options:

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

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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(1d)nSV = C(1 - d)^n Substituting the values: SV=10,00,000×(10.10)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)150.205891132(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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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