Mathematics of FinanceMCQPYQ Nov 19Question 1203 of 512
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Scrap value of a machine valued at Rs. 10,00,000\displaystyle \text{Rs. }10,00,000, after 10\displaystyle 10 years within depreciation at 10%\displaystyle 10\% p.a.:

Options

ARs. 3,48,678.44\displaystyle \text{Rs. }3,48,678.44
BRs. 3,84,679.45\displaystyle \text{Rs. }3,84,679.45
CRs. 4,00,000\displaystyle \text{Rs. }4,00,000
DRs. 3,00,000\displaystyle \text{Rs. }3,00,000
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Correct Answer

Option aRs. 3,48,678.44\displaystyle \text{Rs. }3,48,678.44

All Options:

  • ARs. 3,48,678.44\displaystyle \text{Rs. }3,48,678.44
  • BRs. 3,84,679.45\displaystyle \text{Rs. }3,84,679.45
  • CRs. 4,00,000\displaystyle \text{Rs. }4,00,000
  • DRs. 3,00,000\displaystyle \text{Rs. }3,00,000

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Detailed Solution & Explanation

**Derivation of Scrap Value** Given: - Initial Value of Machine (V0\displaystyle V_0) = Rs. 10,00,000\displaystyle \text{Rs. }10,00,000 - Rate of Depreciation (d\displaystyle d) = 10%\displaystyle 10\% per annum - Time (t\displaystyle t) = 10\displaystyle 10 years **Step 1: Use the depreciation formula** Vt=V0(1d)tV_t = V_0(1 - d)^t V10=1000000(10.10)10V_{10} = 1000000(1 - 0.10)^{10} V10=1000000(0.9)10V_{10} = 1000000(0.9)^{10} **Step 2: Compute the value** (0.9)100.34867844(0.9)^{10} \approx 0.34867844 V10=1000000×0.34867844=Rs. 3,48,678.44V_{10} = 1000000 \times 0.34867844 = \text{Rs. }3,48,678.44 Hence, **Option A** 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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