To determine the effective annual interest rate when the nominal interest rate is compounded more frequently than annually, we can use the following formula:

$\text{Effective Interest Rate} = \left(1 + \frac{i}{n}\right)^n - 1$

where:

• $i$ is the nominal annual interest rate
• $n$ is the number of compounding periods per year

Given:

• Nominal interest rate ($i$) = 16.5% per annum = 0.165
• Compounding frequency ($n$) = 6 times per year (since it compounds every second month)

Now, we substitute these values into the formula:

$\text{Effective Interest Rate} = \left(1 + \frac{0.165}{6}\right)^6 - 1$

Let's calculate this step by step:

1. Divide the nominal rate by the number of compounding periods:

$\frac{0.165}{6} = 0.0275$

2. Add 1 to this value:

$1 + 0.0275 = 1.0275$

3. Raise this result to the power of the number of compounding periods:

$1.0275^6$

Using a calculator:

$1.0275^6 \approx 1.171659$

4. Subtract 1 from this result to find the effective interest rate:

$1.171659 - 1 = 0.171659$

5. Convert this to a percentage:

$0.171659 \times 100 \approx 17.17\%$

So, the effective annual interest rate is approximately 17.17%.

Would you like more details or have any questions about this process?

Here are some related questions for further understanding:

1. What is the difference between nominal and effective interest rates?
2. How would the effective interest rate change if the compounding frequency increased to monthly?
3. Can you explain the concept of compound interest?
4. What is the formula for continuous compounding, and how does it differ from discrete compounding?
5. How do you convert an effective interest rate to a nominal rate?
6. Why is the effective interest rate always higher than the nominal rate when compounded more than once a year?
7. What are some practical applications of understanding effective interest rates?
8. How would the effective interest rate calculation change if the nominal rate was different?

Tip: When comparing different financial products, always look at the effective interest rate rather than the nominal rate, as it gives a true picture of the actual interest earned or paid.