Mathematics of FinanceMCQPYQ Nov. 20Question 1438 of 512
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Present value of a scooter is 7,290\displaystyle ₹ 7,290 if its value decrease every year by 10%\displaystyle 10\% then its value before 3\displaystyle 3 years is equal to:

Options

A10,000\displaystyle 10,000
B10,500\displaystyle 10,500
C20,000\displaystyle 20,000
D20,500\displaystyle 20,500
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Correct Answer

Option a10,000\displaystyle 10,000

All Options:

  • A10,000\displaystyle 10,000
  • B10,500\displaystyle 10,500
  • C20,000\displaystyle 20,000
  • D20,500\displaystyle 20,500

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Detailed Solution & Explanation

Let the value of the scooter 3\displaystyle 3 years ago be P0\displaystyle P_0. Given parameters: * Present Value (PV\displaystyle PV) = Rs. 7,290\displaystyle \text{Rs. }7,290 * 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: 7,290=P0(10.10)37,290 = P_0 (1 - 0.10)^3 7,290=P0(0.9)37,290 = P_0 (0.9)^3 7,290=P0×0.7297,290 = P_0 \times 0.729 Solving for P0\displaystyle P_0: P0=7,2900.729=10,000P_0 = \frac{7,290}{0.729} = 10,000 Thus, the value of the scooter 3\displaystyle 3 years ago was Rs. 10,000\displaystyle \text{Rs. }10,000. 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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