Mathematics of FinanceMCQMTP Mar 22Question 1347 of 512
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Present value of a scooter is 7,290\displaystyle 7,290. Its value decreases every year by 10%\displaystyle 10\% then the 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

**Derivation of Scooter Value 3 Years Ago** Given: - Present Value (Vt\displaystyle V_t) = Rs. 7,290\displaystyle \text{Rs. }7,290 - Time (t\displaystyle t) = 3\displaystyle 3 years - Rate of Depreciation (d\displaystyle d) = 10%\displaystyle 10\% per annum **Step 1: Set up the depreciation formula** Vt=V0(1d)tV_t = V_0(1 - d)^t 7290=V0(10.10)37290 = V_0(1 - 0.10)^3 7290=V0(0.9)37290 = V_0(0.9)^3 7290=0.729V07290 = 0.729 V_0 **Step 2: Solve for V0\displaystyle V_0** V0=72900.729=Rs. 10,000V_0 = \frac{7290}{0.729} = \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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