Mathematics of FinanceMCQMTP Oct 22Question 1342 of 512
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A Maruti Zen cost $3,60,000\displaystyle . Its price depreciates at the rate of $10\% p.a. during the first two years and at the rate of $20\%$ in third year. Also find the total depreciation.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $1,26,720$

All Options:

  • A$1,26,720$
  • B$1,15,620$
  • C$1,25,000$
  • D$1,10,520$

Detailed Solution & Explanation

**Derivation of Total Depreciation** Given: - Initial Cost (V0\displaystyle V_0) = Rs. 3,60,000\displaystyle Rs. \displaystyle \text{Rs. }3,60,000 - Depreciation rate for first two years (d1\displaystyle d_1) = $10\%$ p.a. - Depreciation rate for third year (d2\displaystyle d_2) = $20\%$ p.a. **Step 1: Calculate the depreciated value after 2 years (V2\displaystyle V_2)** V2=V0(1−d1)2V_2 = V_0(1 - d_1)^2 V2=360000(1−0.10)2V_2 = 360000(1 - 0.10)^2 V2=360000(0.9)2V_2 = 360000(0.9)^2 V2=360000×0.81=Rs. 2,91,600V_2 = 360000 ×\displaystyle \times 0.81 = Rs. \displaystyle \text{Rs. }2,91,600 **Step 2: Calculate the depreciated value after 3 years (V3\displaystyle V_3)** V3=V2(1−d2)V_3 = V_2(1 - d_2) V3=291600(1−0.20)V_3 = 291600(1 - 0.20) V3=291600×0.80=Rs. 2,33,280V_3 = 291600 ×\displaystyle \times 0.80 = Rs. \displaystyle \text{Rs. }2,33,280 **Step 3: Calculate the total depreciation amount** Total Depreciation=V0−V3Total Depreciation=V0−V3\displaystyle \text{Total Depreciation} = V_0 - V_3 Total Depreciation=360000−233280=Rs. 1,26,720\displaystyle \text{Total Depreciation} = 360000 - 233280 = \text{Rs. }1,26,720 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

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

Key Concepts to Understand

Depreciation

Allocation of the cost of a tangible fixed asset over its useful life due to wear and tear, efflux of time, or obsolescence.

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