Mathematics of FinanceMCQPYQ Nov 18Question 1436 of 512
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The value of furniture depreciates by 10%\displaystyle 10\% a year, it the present value of the furniture in an office is 21,870\displaystyle 21,870. Calculate the value of furniture 3\displaystyle 3 years ago

Options

A30,000\displaystyle 30,000
B35,000\displaystyle 35,000
C40,000\displaystyle 40,000
D50,000\displaystyle 50,000
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Correct Answer

Option a30,000\displaystyle 30,000

All Options:

  • A30,000\displaystyle 30,000
  • B35,000\displaystyle 35,000
  • C40,000\displaystyle 40,000
  • D50,000\displaystyle 50,000

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Detailed Solution & Explanation

Let the value of the furniture 3\displaystyle 3 years ago be P0\displaystyle P_0. Given parameters: * Present Value (PV\displaystyle PV) = Rs. 21,870\displaystyle \text{Rs. }21,870 * Rate of depreciation (d\displaystyle d) = 10%\displaystyle 10\% p.a. =0.10\displaystyle = 0.10 * Time (n\displaystyle n) = 3\displaystyle 3 years The formula for depreciated value is: PV=P0(1d)nPV = P_0 (1 - d)^n Substituting the values: 21,870=P0(10.10)321,870 = P_0 (1 - 0.10)^3 21,870=P0(0.9)321,870 = P_0 (0.9)^3 21,870=P0×0.72921,870 = P_0 \times 0.729 Solving for P0\displaystyle P_0: P0=21,8700.729=30,000P_0 = \frac{21,870}{0.729} = 30,000 Thus, the value of the furniture 3\displaystyle 3 years ago was Rs. 30,000\displaystyle \text{Rs. }30,000. (Note: While Option B is marked as correct in some study keys, the exact calculation yields 30,000, which is 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.

View Official ICAI Syllabus

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