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

Options

A10.5%\displaystyle 10.5\%
B10%\displaystyle 10\%
C15%\displaystyle 15\%
D14%\displaystyle 14\%
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Correct Answer

✅ Option b — 10%\displaystyle 10\%

All Options:

  • A10.5%\displaystyle 10.5\%
  • B10%\displaystyle 10\%
  • C15%\displaystyle 15\%
  • D14%\displaystyle 14\%

Detailed Solution & Explanation

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

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