Mathematics of FinanceMCQPYQ Nov 18Question 1182 of 512
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If in two years' time a principal of Rs. 100\displaystyle Rs. \displaystyle \text{Rs. }100 amounts to Rs. 121\displaystyle Rs. \displaystyle \text{Rs. }121 when the interest at r%\displaystyle r\% is compounded annually, then the value of r\displaystyle r is

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

✅ Option b — $10\%$

All Options:

  • A$10.5\%$
  • B$10\%$
  • C$15\%$
  • D$14\%$

Detailed Solution & Explanation

**Derivation of Rate of Interest** Given: - Principal (P\displaystyle P) = Rs. 100\displaystyle Rs. \displaystyle \text{Rs. }100 - Amount (A\displaystyle A) = Rs. 121\displaystyle Rs. \displaystyle \text{Rs. }121 - Time (t\displaystyle t) = 2\displaystyle 2 years - Compounded annually **Step 1: Set up the Compound Interest equation** A=P(1+r100)tA = P\left(1 + r100\displaystyle \frac{r}{100}\right)^t 121=100(1+r100)2121 = 100\left(1 + r100\displaystyle \frac{r}{100}\right)^2 **Step 2: Solve for r\displaystyle r** 121100=(1+r100)2\displaystyle \frac{121}{100} = \left(1 + r100\displaystyle \frac{r}{100}\right)^2 1.21=(1+r100)21.21 = \left(1 + r100\displaystyle \frac{r}{100}\right)^2 Taking the square root of both sides: 1.21=1+r1001.21=1+r100\displaystyle \sqrt{1.21} = 1 + \frac{r}{100} 1.1=1+r1001.1 = 1 + r100\displaystyle \frac{r}{100} r100=1.1−1r100=1\displaystyle \frac{r}{100} = 1.1 - 1 r100=0.1  ⟹  r=10% per annumr100=0\displaystyle \frac{r}{100} = 0.1 \implies r = 10\%  per annum\displaystyle \text{ per annum} Hence, **Option B** 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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