Mathematics for FinancePYQ Nov 18Question 1280 of 512
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The effective rate of interest on an amount 25,000\displaystyle 25,000 is deposited in a bank for one year at value of 6%\displaystyle 6\% per annum compounded semi-annually is

Options

A5.99%\displaystyle 5.99\%
B5.95%\displaystyle 5.95\%
C6.09%\displaystyle 6.09\%
D6.90%\displaystyle 6.90\%
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Correct Answer

✅ Option c — 6.09%\displaystyle 6.09\%

All Options:

  • A5.99%\displaystyle 5.99\%
  • B5.95%\displaystyle 5.95\%
  • C6.09%\displaystyle 6.09\%
  • D6.90%\displaystyle 6.90\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Principal (P\displaystyle P) = Rs. 25,000\displaystyle \text{Rs. }25,000 (Note: Effective rate is independent of principal) - Nominal Rate (r\displaystyle r) = 6%\displaystyle 6\% per annum compounded semi-annually **Step 1: Calculate periodic rate (i\displaystyle i) and number of periods (m\displaystyle m)** - Periodic rate i=r2=6%2=3%=0.03\displaystyle i = \frac{r}{2} = \frac{6\%}{2} = 3\% = 0.03 per half-year. - Compounding periods per year m=2\displaystyle m = 2. **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 C** is the correct answer.

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