Mathematics of FinanceMCQPYQ May 19 Series II, ICAI SMQuestion 1289 of 512
All Questions

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 d11.49%\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\%

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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)m1E = \left(1 + \frac{r}{m}\right)^m - 1 0.11=(1+r4)410.11 = \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+r41.026431 + \frac{r}{4} \approx 1.02643 r40.02643\frac{r}{4} \approx 0.02643 r0.1057 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)41=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.

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

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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