Mathematics of FinanceMCQMTP May 19Question 1492 of 512
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The furniture depreciates by 10%\displaystyle 10\% p.a. If the present value of the furniture in office is 21870\displaystyle 21870, calculate the value of furniture 3\displaystyle 3 years ago.

Options

A30000\displaystyle 30000
B35000\displaystyle 35000
C40000\displaystyle 40000
D45000\displaystyle 45000
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Correct Answer

Option c40000\displaystyle 40000

All Options:

  • A30000\displaystyle 30000
  • B35000\displaystyle 35000
  • C40000\displaystyle 40000
  • D45000\displaystyle 45000

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Detailed Solution & Explanation

Let the value of the furniture 3\displaystyle 3 years ago be P\displaystyle P. The rate of depreciation is d=10%\displaystyle d = 10\% p.a. The present value is given by: PV=P(1d)nPV = P(1 - d)^n Substituting the values: 21,870=P(10.10)321,870 = P(1 - 0.10)^3 21,870=P(0.9)321,870 = P(0.9)^3 21,870=P×0.72921,870 = P \times 0.729 Solving for P\displaystyle P: P=21,8700.729=30,000P = \frac{21,870}{0.729} = 30,000 Thus, the value of the furniture 3\displaystyle 3 years ago was Rs. 30,000\displaystyle 30,000 (Option A). However, the official key marks Option C. 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.

View Official ICAI Syllabus

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