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

Options

A49490\displaystyle 49490
B59049\displaystyle 59049
C61029\displaystyle 61029
D51049\displaystyle 51049
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Correct Answer

Option d51049\displaystyle 51049

All Options:

  • A49490\displaystyle 49490
  • B59049\displaystyle 59049
  • C61029\displaystyle 61029
  • D51049\displaystyle 51049

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Detailed Solution & Explanation

The Scrap Value (SV\displaystyle SV) after depreciation is given by: SV=C(1d)nSV = C(1 - d)^n Given: * Initial value (C\displaystyle C) = 1,00,000\displaystyle 1,00,000 * Depreciation rate (d\displaystyle d) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 * Time (n\displaystyle n) = 5\displaystyle 5 years Substituting the values: SV=1,00,000×(10.10)5=1,00,000×0.59049=59,049SV = 1,00,000 \times (1 - 0.10)^5 = 1,00,000 \times 0.59049 = 59,049 Mathematically, this corresponds to Option B. However, the official key marks Option D (51,049\displaystyle 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

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