The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

### Concept & Effective Annual Rate (EAR) When interest is compounded more than once a year, the effective annual rate (EAR) is higher than the nominal annual rate due to compounding. $$EAR = \left(1 + \frac{R}{n \times 100}\right)^n - 1$$ ### Step-by-Step Solution 1. **Identify the given values:** Nominal annual rate = 6% Compounding frequency = half-yearly ($n = 2$) 2. **Determine half-yearly rate:** Rate per half-year = $\frac{6\%}{2} = 3\%$ 3. **Calculate effective rate for two periods (1 year):** Equivalent multiplier = $\left(1 + \frac{3}{100}\right)^2 = (1.03)^2$ $(1.03)^2 = 1.0609$ 4. **Convert to percentage:** Effective rate = $(1.0609 - 1) \times 100\% = 0.0609 \times 100\% = 6.09\%$ ### Exam Strategy & Shortcut Use the successive percentage formula for 2 periods: $A + B + \frac{A \times B}{100}$. Here, $A = 3\%$, $B = 3\%$. Effective Rate = $3 + 3 + \frac{3 \times 3}{100} = 6 + 0.09 = 6.09\%$. ### Common Pitfall Misunderstanding "nominal rate". Some students mistakenly apply the 6% rate twice, yielding $6 + 6 + 0.36 = 12.36\%$, failing to divide the annual rate by the number of compounding periods first. ### Final Answer Therefore, the correct answer is **6.09%**.