Mathematics of FinancePYQ May 25Question 4012 of 507
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The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

Options

A6.06%
B6.07%
C6.08%
D6.09%
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Correct Answer

Option d6.09%

All Options:

  • A6.06%
  • B6.07%
  • C6.08%
  • D6.09%

Detailed Solution & Explanation

The relationship between the nominal rate of interest (r\displaystyle r) and the effective rate of interest (E\displaystyle E) compounded half-yearly is given by:
E=(1+r2)21E = \left(1 + \frac{r}{2}\right)^2 - 1
Given that the nominal annual rate of interest is 6%\displaystyle 6\%, which means r=0.06\displaystyle r = 0.06.
Substitute r=0.06\displaystyle r = 0.06 into the formula:
E=(1+0.062)21E = \left(1 + \frac{0.06}{2}\right)^2 - 1
E=(1+0.03)21E = (1 + 0.03)^2 - 1
E=(1.03)21E = (1.03)^2 - 1
E=1.06091E = 1.0609 - 1
E=0.0609=6.09%E = 0.0609 = 6.09\%
Hence, the effective annual rate of interest is 6.09%\displaystyle 6.09\%.
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

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