Mathematics for FinancePYQ Nov 19Question 1198 of 512
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Find the effective rate of interest on Rs. 10,000\displaystyle \text{Rs. }10,000 on which interest is payable half yearly at 5%\displaystyle 5\% p.a.

Options

A5.06%\displaystyle 5.06\%
B4%\displaystyle 4\%
C0.4%\displaystyle 0.4\%
D3%\displaystyle 3\%
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Correct Answer

✅ Option a — 5.06%\displaystyle 5.06\%

All Options:

  • A5.06%\displaystyle 5.06\%
  • B4%\displaystyle 4\%
  • C0.4%\displaystyle 0.4\%
  • D3%\displaystyle 3\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Principal (P\displaystyle P) = Rs. 10,000\displaystyle \text{Rs. }10,000 (Note: The effective rate of interest does not depend on the principal) - Nominal Rate (r\displaystyle r) = 5%\displaystyle 5\% per annum - Compounding Frequency = Half-yearly (m=2\displaystyle m = 2) **Step 1: Find periodic interest rate (i\displaystyle i)** i=rm=5%2=2.5%=0.025 per periodi = \frac{r}{m} = \frac{5\%}{2} = 2.5\% = 0.025 \text{ per period} **Step 2: Calculate the effective rate of interest (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.025)2−1E = (1 + 0.025)^2 - 1 E=(1.025)2−1E = (1.025)^2 - 1 E=1.050625−1=0.050625 or 5.0625%≈5.06%E = 1.050625 - 1 = 0.050625 \text{ or } 5.0625\% \approx 5.06\% Hence, **Option A** is the correct answer.

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