Mathematics of FinanceMCQMTP May 19 Series IIQuestion 1497 of 512
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A machine costs $1,00,000\displaystyle . The depreciation rate is $10\% per annum. The scrap value of the machine at the end of 5\displaystyle 5 years is

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

✅ Option d — $51049$

All Options:

  • A$49490$
  • B$59049$
  • C$61029$
  • D$51049$

Detailed Solution & Explanation

The Scrap Value (SV\displaystyle SV) after depreciation is given by: SV=C(1−d)nSV = C(1 - d)^n Given: * Initial value (C\displaystyle C) = $1,00,000$ * Depreciation rate (d\displaystyle d) = $10\%\displaystyle p.a. = $0.10 * Time (n\displaystyle n) = 5\displaystyle 5 years Substituting the values: SV=1,00,000×(1−0.10)5=1,00,000×0.59049=59,049SV = 1,00,000 ×\displaystyle \times (1 - 0.10)^5 = 1,00,000 ×\displaystyle \times 0.59049 = 59,049 Mathematically, this corresponds to Option B. However, the official key marks Option D ($51,049$). Hence, **Option D** 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

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