Mathematics for FinancePYQ Dec 22Question 1238 of 512
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The effective annual rate of interest corresponding to a normal rate of 6%\displaystyle 6\% per annum payable half yearly is:

Options

A6.06%\displaystyle 6.06\%
B6.07%\displaystyle 6.07\%
C6.08%\displaystyle 6.08\%
D6.09%\displaystyle 6.09\%
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Correct Answer

✅ Option d — 6.09%\displaystyle 6.09\%

All Options:

  • A6.06%\displaystyle 6.06\%
  • B6.07%\displaystyle 6.07\%
  • C6.08%\displaystyle 6.08\%
  • D6.09%\displaystyle 6.09\%

Detailed Solution & Explanation

**Derivation of Effective Annual Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 6%\displaystyle 6\% per annum - Compounding Frequency = Half-yearly (m=2\displaystyle m = 2) **Step 1: Find the periodic interest rate (i\displaystyle i)** i=rm=6%2=3%=0.03 per half-yeari = \frac{r}{m} = \frac{6\%}{2} = 3\% = 0.03 \text{ per half-year} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.03)2−1E = (1 + 0.03)^2 - 1 E=(1.03)2−1E = (1.03)^2 - 1 E=1.0609−1=0.0609 or 6.09%E = 1.0609 - 1 = 0.0609 \text{ or } 6.09\% Hence, **Option D** is the correct answer.

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