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 after 15 years of depreciation is $10\% p.a.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option b — $205891.13$

All Options:

  • A$215891.13$
  • B$205891.13$
  • C$225891.13$
  • DNone

Detailed Solution & Explanation

Given parameters: * Initial Value of the machine (C\displaystyle C) = Rs. 10,00,000\displaystyle Rs. \displaystyle \text{Rs. }10,00,000 * Rate of depreciation (d\displaystyle d) = $10\%p.a.\displaystyle p.a.= 0.10$ * Time (n\displaystyle n) = $15$ 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 ×\displaystyle \times (1 - 0.10)^{15} SV=10,00,000×(0.9)15SV = 10,00,000 ×\displaystyle \times (0.9)^{15} First, let's calculate (0.9)15\displaystyle (0.9)^{15}: (0.9)15≈0.205891132(0.9)^{15} ≈\displaystyle \approx 0.205891132 Now substitute this back: SV=10,00,000×0.205891132=2,05,891.13SV = 10,00,000 ×\displaystyle \times 0.205891132 = 2,05,891.13 Thus, the scrap value is approximately Rs. 2,05,891.13\displaystyle Rs. \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.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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.

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