Mathematics of FinanceMCQMTP Apr 21Question 1325 of 512
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The cost of machinery Rs.1,25,000\displaystyle 1,25,000 if its useful life estimated to the 20\displaystyle 20 years and the rate of depreciation of its cost is 10%\displaystyle 10\% p.a. Then scrap value of machinery is

Options

ARs.15,187\displaystyle 15,187
BRs.15,400\displaystyle 15,400
CRs.15,300\displaystyle 15,300
DRs.15,250\displaystyle 15,250
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Correct Answer

Option aRs.15,187\displaystyle 15,187

All Options:

  • ARs.15,187\displaystyle 15,187
  • BRs.15,400\displaystyle 15,400
  • CRs.15,300\displaystyle 15,300
  • DRs.15,250\displaystyle 15,250

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Detailed Solution & Explanation

**Derivation of Machine Scrap Value** Given: - Initial Cost (V0\displaystyle V_0) = Rs. 1,25,000\displaystyle \text{Rs. }1,25,000 - Estimated useful life (t\displaystyle t) = 20\displaystyle 20 years - Depreciation Rate (d\displaystyle d) = 10%\displaystyle 10\% per annum **Step 1: Set up the depreciation formula** Vt=V0(1d)tV_t = V_0(1 - d)^t Vt=125000(10.10)20V_t = 125000(1 - 0.10)^{20} Vt=125000(0.9)20V_t = 125000(0.9)^{20} **Step 2: Compute the value** (0.9)200.12157665(0.9)^{20} \approx 0.12157665 Vt=125000×0.12157665Rs. 15,197V_t = 125000 \times 0.12157665 \approx \text{Rs. }15,197 *(Note: Option A is listed as Rs. 15,187, which is closest to the mathematical value and matches the textbook's key. We accept Option A.)* 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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