Mathematics of FinanceMCQPYQ Nov 19Question 1370 of 512
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The difference in simple interest of a sum invested of Rs. 1,500\displaystyle \text{Rs. }1,500 for 3\displaystyle 3 years is Rs. 18\displaystyle \text{Rs. }18. The difference in their rates is

Options

A0.4\displaystyle 0.4
B0.6\displaystyle 0.6
C0.8\displaystyle 0.8
D0.10\displaystyle 0.10
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Correct Answer

Option a0.4\displaystyle 0.4

All Options:

  • A0.4\displaystyle 0.4
  • B0.6\displaystyle 0.6
  • C0.8\displaystyle 0.8
  • D0.10\displaystyle 0.10

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Detailed Solution & Explanation

**Derivation of Difference in Interest Rates** Given: - Principal (P\displaystyle P) = Rs. 1,500\displaystyle \text{Rs. }1,500 - Time (t\displaystyle t) = 3\displaystyle 3 years - Difference in Simple Interest = Rs. 18\displaystyle \text{Rs. }18 **Step 1: Set up the formula for difference in Simple Interest** Let the two rates be r1\displaystyle r_1 and r2\displaystyle r_2. SI1SI2=P×r1×t100P×r2×t100SI_1 - SI_2 = \frac{P \times r_1 \times t}{100} - \frac{P \times r_2 \times t}{100} 18=1500×(r1r2)×310018 = \frac{1500 \times (r_1 - r_2) \times 3}{100} **Step 2: Solve for (r1r2)\displaystyle (r_1 - r_2)** 18=15×3×(r1r2)18 = 15 \times 3 \times (r_1 - r_2) 18=45(r1r2)18 = 45 (r_1 - r_2) r1r2=1845=25=0.4%r_1 - r_2 = \frac{18}{45} = \frac{2}{5} = 0.4\% 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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