Mathematics of FinanceMCQMTP June 22Question 1355 of 512
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The present value of a scooter is 7290\displaystyle 7290. The rate of depreciation is 10%\displaystyle 10\%. What was its value 3\displaystyle 3 years ago?

Options

A10000\displaystyle 10000
B10010\displaystyle 10010
C9990\displaystyle 9990
D12000\displaystyle 12000
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Correct Answer

Option a10000\displaystyle 10000

All Options:

  • A10000\displaystyle 10000
  • B10010\displaystyle 10010
  • C9990\displaystyle 9990
  • D12000\displaystyle 12000

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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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