Mathematics of FinanceMCQPYQ Nov 18Question 1280 of 512
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The effective rate of interest on an amount 25,000\displaystyle 25,000 is deposited in a bank for one year at value of 6%\displaystyle 6\% per annum compounded semi-annually is

Options

A5.99%\displaystyle 5.99\%
B5.95%\displaystyle 5.95\%
C6.09%\displaystyle 6.09\%
D6.90%\displaystyle 6.90\%
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Correct Answer

Option c6.09%\displaystyle 6.09\%

All Options:

  • A5.99%\displaystyle 5.99\%
  • B5.95%\displaystyle 5.95\%
  • C6.09%\displaystyle 6.09\%
  • D6.90%\displaystyle 6.90\%

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Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Principal (P\displaystyle P) = Rs. 25,000\displaystyle \text{Rs. }25,000 (Note: Effective rate is independent of principal) - Nominal Rate (r\displaystyle r) = 6%\displaystyle 6\% per annum compounded semi-annually **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (m\displaystyle m)** - Periodic rate i=r2=6%2=3%=0.03\displaystyle i = \frac{r}{2} = \frac{6\%}{2} = 3\% = 0.03 per half-year. - Compounding periods per year m=2\displaystyle m = 2. **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m1E = (1 + i)^m - 1 E=(1+0.03)21E = (1 + 0.03)^2 - 1 E=(1.03)21E = (1.03)^2 - 1 E=1.06091=0.0609 or 6.09%E = 1.0609 - 1 = 0.0609 \text{ or } 6.09\% Hence, **Option C** 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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