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

Options

A. 0.0606
B. 0.0607
C. 0.0608
D. 0.0609

Answer

To find the effective annual rate of interest corresponding to a nominal rate of 6% per annum, payable half-yearly, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the nominal interest rate and the compounding frequency:**
- The nominal interest rate is 6% per annum.
- Since it is payable half-yearly, we will divide the nominal rate by 2.

\[ \text{Half-yearly rate} = \frac{6\%}{2} = 3\% \]

2. **Use the formula for effective annual rate (EAR):**
- The formula for calculating the effective annual rate when compounding occurs multiple times a year is:

\[ \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 \]
where \( r \) is the nominal rate (as a decimal) and \( n \) is the number of compounding periods per year.

3. **Convert the half-yearly rate to decimal:**
- Convert 3% to decimal:

\[ r = \frac{3}{100} = 0.03 \]
- Since compounding occurs twice a year (half-yearly), \( n = 2 \).

4. **Substitute the values into the formula:**
- Plugging in the values into the EAR formula:

\[ \text{EAR} = \left(1 + 0.03\right)^2 - 1 \]

5. **Calculate the expression:**
- Calculate \( (1 + 0.03)^2 \):

\[ (1.03)^2 = 1.0609 \]
- Now subtract 1:

\[ \text{EAR} = 1.0609 - 1 = 0.0609 \]

6. **Convert the result back to percentage:**
- To express the effective annual rate as a percentage:

\[ \text{EAR} = 0.0609 \times 100 = 6.09\% \]

### Final Answer:
The effective annual rate of interest corresponding to a nominal rate of 6% per annum, payable half-yearly, is **6.09%**.

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