A bank account pays an annual interest rate of 7.06%. Interest payments are made every four months. What is the effective interest rate for 4 months?

To calculate the effective interest rate for a four-month period when given an annual interest rate, you can use the following formula:

\[
\text{Effective Interest Rate} = \left(1 + \frac{r_{\text{annual}}}{n}\right)^n - 1
\]

where:
- \( r_{\text{annual}} \) is the annual interest rate,
- \( n \) is the number of compounding periods in a year.

However, since we want the interest rate for a single four-month period, we'll modify the formula:

\[
\text{Effective Interest Rate} = \left(1 + \frac{r_{\text{annual}}}{n}\right)^k - 1
\]

where:
- \( r_{\text{annual}} = 7.06\% \) or 0.0706,
- \( n = 3 \) (since there are 3 four-month periods in a year),
- \( k = 1 \) (because we want the interest for one four-month period).

Now, substitute the values:

\[
\text{Effective Interest Rate} = \left(1 + \frac{0.0706}{3}\right)^1 - 1
\]

Simplify the expression:

\[
\text{Effective Interest Rate} = \left(1 + 0.0235333\right) - 1
\]

\[
\text{Effective Interest Rate} = 1.0235333 - 1 = 0.0235333
\]

Convert it to a percentage:

\[
\text{Effective Interest Rate} \approx 2.35\%
\]

So, the effective interest rate for a four-month period is **2.35%**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the effective interest rate change if the compounding frequency were monthly?
2. What is the effective annual interest rate for an account that compounds every four months at 7.06% annually?
3. How do you calculate the interest earned over a specific period using the effective interest rate?
4. What is the difference between nominal and effective interest rates?
5. How does the effective interest rate for different compounding periods compare?

**Tip:** When calculating the effective interest rate for a period shorter than a year, divide the annual rate by the number of periods within the year.

Learn how to calculate the effective interest rate for a four-month period when given a 7.06% annual interest rate. This problem involves understanding compound interest and the formula for effective interest rate calculations.

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