Mathematics for FinanceMTP Mar 21Question 1317 of 512
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The effective rate equivalent to nominal rate of 6%\displaystyle 6\% compounded monthly is:

Options

A6.05\displaystyle 6.05
B6.17\displaystyle 6.17
C6.26\displaystyle 6.26
D6.07\displaystyle 6.07
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Correct Answer

✅ Option b — 6.17\displaystyle 6.17

All Options:

  • A6.05\displaystyle 6.05
  • B6.17\displaystyle 6.17
  • C6.26\displaystyle 6.26
  • D6.07\displaystyle 6.07

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal rate (r\displaystyle r) = 6%\displaystyle 6\% per annum - Compounding Frequency = Compounded monthly (m=12\displaystyle m = 12) **Step 1: Find the monthly interest rate (i\displaystyle i)** i=rm=6%12=0.5%=0.005 per monthi = \frac{r}{m} = \frac{6\%}{12} = 0.5\% = 0.005 \text{ per month} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.005)12−1E = (1 + 0.005)^{12} - 1 E=(1.005)12−1E = (1.005)^{12} - 1 E≈1.061678−1=0.061678 or 6.17%E \approx 1.061678 - 1 = 0.061678 \text{ or } 6.17\% Hence, **Option B** is the correct answer.

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