Mathematics of FinanceMCQPYQ Nov 18Question 1278 of 512
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The value of a machine depreciates 12%\displaystyle 12\% annually. If the present value of 68,150\displaystyle 68,150 then its value in 3\displaystyle 3 years ago was.

Options

A1,10,000\displaystyle 1,10,000
B1,00,004\displaystyle 1,00,004
C92,000\displaystyle 92,000
D97,900\displaystyle 97,900
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Correct Answer

Option b1,00,004\displaystyle 1,00,004

All Options:

  • A1,10,000\displaystyle 1,10,000
  • B1,00,004\displaystyle 1,00,004
  • C92,000\displaystyle 92,000
  • D97,900\displaystyle 97,900

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Detailed Solution & Explanation

**Derivation of Original Value (3 Years Ago)** Given: - Present Value (Vt\displaystyle V_t) = Rs. 68,150\displaystyle \text{Rs. }68,150 - Rate of Depreciation (d\displaystyle d) = 12%\displaystyle 12\% annually - Time (t\displaystyle t) = 3\displaystyle 3 years **Step 1: Set up the depreciation formula** Vt=V0(1d)tV_t = V_0(1 - d)^t 68150=V0(10.12)368150 = V_0(1 - 0.12)^3 68150=V0(0.88)368150 = V_0(0.88)^3 68150=0.681472V068150 = 0.681472 V_0 **Step 2: Solve for V0\displaystyle V_0** V0=681500.681472Rs. 1,00,004V_0 = \frac{68150}{0.681472} \approx \text{Rs. }1,00,004 Hence, **Option B** 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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