Mathematics for FinancePYQ 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 b — 26.82%\displaystyle 26.82\%

All Options:

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

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)m−1E = (1 + i)^m - 1 E=(1+0.02)12−1E = (1 + 0.02)^{12} - 1 E=(1.02)12−1E = (1.02)^{12} - 1 **Step 3: Compute the value** (1.02)12≈1.268242(1.02)^{12} \approx 1.268242 E≈1.268242−1=0.268242 or 26.82%E \approx 1.268242 - 1 = 0.268242 \text{ or } 26.82\% Hence, **Option B** is the correct answer.

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