Mathematics of FinanceMCQPYQ Dec 23Question 1254 of 512
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A machine costing $1,00,000$ has useful life of $10$ years. If the rate of depreciation is $12\%$ what is scrap value of the machine at the end of life? Given $(0.88)^{10} = 0.27850$

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

✅ Option c — $27,850$

All Options:

  • A$25,850$
  • B$26,850$
  • C$27,850$
  • D$28,850$

Detailed Solution & Explanation

**Derivation of Scrap Value** Given: - Initial Cost of Machine (V0\displaystyle V_0) = Rs. 1,00,000\displaystyle Rs. \displaystyle \text{Rs. }1,00,000 - Useful Life (t\displaystyle t) = $10$ years - Rate of Depreciation (d\displaystyle d) = $12\%$ per annum - Given: (0.88)10=0.27850\displaystyle (0.88)^{10} = 0.27850 **Step 1: Calculate Scrap Value (Vt\displaystyle V_t)** Vt=V0(1−d)tV_t = V_0(1 - d)^t V10=100000(1−0.12)10V_{10} = 100000(1 - 0.12)^{10} V10=100000(0.88)10V_{10} = 100000(0.88)^{10} Using the given value: V10=100000×0.27850=Rs. 27,850V_{10} = 100000 ×\displaystyle \times 0.27850 = Rs. \displaystyle \text{Rs. }27,850 Hence, **Option C** 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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