Mathematics of FinanceMCQMTP June 24 Series IQuestion 1409 of 512
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The effective annual rate of interest corresponding to nominal rate 6%\displaystyle 6\% p.a. payable quarterly is:

Options

A6.14%\displaystyle 6.14\%
B6.07%\displaystyle 6.07\%
C6.08%\displaystyle 6.08\%
D6.09%\displaystyle 6.09\%
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Correct Answer

Option a6.14%\displaystyle 6.14\%

All Options:

  • A6.14%\displaystyle 6.14\%
  • B6.07%\displaystyle 6.07\%
  • C6.08%\displaystyle 6.08\%
  • D6.09%\displaystyle 6.09\%

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Detailed Solution & Explanation

Given parameters: * Nominal rate of interest (r\displaystyle r) = 6%\displaystyle 6\% p.a. =0.06\displaystyle = 0.06 * Compounding frequency (m\displaystyle m) = 4\displaystyle 4 (compounded quarterly) The quarterly interest rate (i\displaystyle i) is: i=rm=0.064=0.015i = \frac{r}{m} = \frac{0.06}{4} = 0.015 The formula for the effective annual rate of interest (E\displaystyle E) is: E=(1+i)m1E = (1 + i)^m - 1 Substituting the values: E=(1+0.015)41E = (1 + 0.015)^4 - 1 E=(1.015)41E = (1.015)^4 - 1 Let's compute (1.015)4\displaystyle (1.015)^4: (1.015)2=1.030225(1.015)^2 = 1.030225 (1.015)4=(1.030225)21.06136355(1.015)^4 = (1.030225)^2 \approx 1.06136355 Thus: E1.061363551=0.06136355=6.14%E \approx 1.06136355 - 1 = 0.06136355 = 6.14\% The effective annual rate of interest is approximately 6.14%\displaystyle 6.14\%. 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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