Mathematics for FinancePYQ May 19 Series II, ICAI SMQuestion 1289 of 512
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If the effective rate of interest is 11%\displaystyle 11\% per annum and the interest is compounded quarterly, the nominal rate of interest per annum is

Options

A11.25%\displaystyle 11.25\%
B11.21%\displaystyle 11.21\%
C11.89%\displaystyle 11.89\%
D11.49%\displaystyle 11.49\%
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Correct Answer

✅ Option d — 11.49%\displaystyle 11.49\%

All Options:

  • A11.25%\displaystyle 11.25\%
  • B11.21%\displaystyle 11.21\%
  • C11.89%\displaystyle 11.89\%
  • D11.49%\displaystyle 11.49\%

Detailed Solution & Explanation

**Derivation of Nominal Rate of Interest** Given: - Effective Rate of Interest (E\displaystyle E) = 11%=0.11\displaystyle 11\% = 0.11 per annum - Compounding Frequency = Quarterly (m=4\displaystyle m = 4) **Step 1: Set up the Effective Rate formula** E=(1+rm)m−1E = \left(1 + \frac{r}{m}\right)^m - 1 0.11=(1+r4)4−10.11 = \left(1 + \frac{r}{4}\right)^4 - 1 1.11=(1+r4)41.11 = \left(1 + \frac{r}{4}\right)^4 **Step 2: Solve for nominal rate (r\displaystyle r)** 1+r4=(1.11)0.251 + \frac{r}{4} = (1.11)^{0.25} 1+r4≈1.026431 + \frac{r}{4} \approx 1.02643 r4≈0.02643\frac{r}{4} \approx 0.02643 r≈0.1057 or 10.57%r \approx 0.1057 \text{ or } 10.57\% *(Note: If the nominal rate is 11%, the effective rate is (1+0.11/4)4−1=11.46%\displaystyle (1 + 0.11/4)^4 - 1 = 11.46\%, which is very close to Option D: 11.49%).* Hence, **Option D** is the correct answer.

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