Mathematics of FinanceMCQPYQ Nov 19Question 1201 of 512
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The value of scooter is Rs. 10,000\displaystyle \text{Rs. }10,000 find its value after 7\displaystyle 7 years if rate of depreciation is 10%\displaystyle 10\% p.a.

Options

ARs. 4,782.96\displaystyle \text{Rs. }4,782.96
BRs. 4,278.69\displaystyle \text{Rs. }4,278.69
CRs. 42,079\displaystyle \text{Rs. }42,079
DRs. 42,000\displaystyle \text{Rs. }42,000
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Correct Answer

Option aRs. 4,782.96\displaystyle \text{Rs. }4,782.96

All Options:

  • ARs. 4,782.96\displaystyle \text{Rs. }4,782.96
  • BRs. 4,278.69\displaystyle \text{Rs. }4,278.69
  • CRs. 42,079\displaystyle \text{Rs. }42,079
  • DRs. 42,000\displaystyle \text{Rs. }42,000

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Detailed Solution & Explanation

**Derivation of Depreciated Value** Given: - Initial Value of Scooter (V0\displaystyle V_0) = Rs. 10,000\displaystyle \text{Rs. }10,000 - Rate of Depreciation (d\displaystyle d) = 10%\displaystyle 10\% per annum - Time (t\displaystyle t) = 7\displaystyle 7 years **Step 1: Set up the depreciation formula** Vt=V0(1d)tV_t = V_0(1 - d)^t V7=10000(10.10)7V_7 = 10000(1 - 0.10)^7 V7=10000(0.9)7V_7 = 10000(0.9)^7 **Step 2: Compute the value** (0.9)70.4782969(0.9)^7 \approx 0.4782969 V7=10000×0.4782969=Rs. 4,782.969Rs. 4,782.96V_7 = 10000 \times 0.4782969 = \text{Rs. }4,782.969 \approx \text{Rs. }4,782.96 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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