Mathematics of FinanceMCQPYQ July 21Question 1222 of 512
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The effective rate of return for 24%\displaystyle 24\% per annum convertible monthly is given as:

Options

A24%\displaystyle 24\%
B26.82%\displaystyle 26.82\%
C18%\displaystyle 18\%
D24.24%\displaystyle 24.24\%
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Correct Answer

Option b26.82%\displaystyle 26.82\%

All Options:

  • A24%\displaystyle 24\%
  • B26.82%\displaystyle 26.82\%
  • C18%\displaystyle 18\%
  • D24.24%\displaystyle 24.24\%

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Detailed Solution & Explanation

**Derivation of Effective Rate of Return** Given: - Nominal interest rate (r\displaystyle r) = 24%\displaystyle 24\% per annum - Compounding Frequency = Convertible monthly (m=12\displaystyle m = 12) **Step 1: Find periodic interest rate (i\displaystyle i)** i=rm=24%12=2%=0.02 per monthi = \frac{r}{m} = \frac{24\%}{12} = 2\% = 0.02 \text{ per month} **Step 2: Calculate the effective rate of interest (E\displaystyle E)** E=(1+i)m1E = (1 + i)^m - 1 E=(1+0.02)121E = (1 + 0.02)^{12} - 1 E=(1.02)121E = (1.02)^{12} - 1 **Step 3: Compute the value** (1.02)121.268242(1.02)^{12} \approx 1.268242 E1.2682421=0.268242 or 26.82%E \approx 1.268242 - 1 = 0.268242 \text{ or } 26.82\% Hence, **Option B** 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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