Calculate the equivalent periodic interest rate per payment interval for the following annuity: Semiannual payments earning 6% compounded monthly.

To calculate the equivalent periodic interest rate per payment interval for an annuity with semiannual payments earning 6% compounded monthly, we need to follow these steps:

1. **Determine the monthly interest rate from the annual rate.**
2. **Convert the monthly interest rate to an equivalent semiannual interest rate.**

### Step 1: Determine the Monthly Interest Rate

The annual interest rate is 6%, compounded monthly. Therefore, the monthly interest rate \( i \) is:
\[ i = \frac{6\%}{12} = 0.5\% \text{ per month} \]

### Step 2: Convert the Monthly Interest Rate to an Equivalent Semiannual Interest Rate

To find the equivalent semiannual interest rate, we need to compound the monthly rate for six months, since there are six months in a semiannual period.

The formula for converting a monthly interest rate to a semiannual interest rate is:
\[ (1 + i)^{6} - 1 \]

Where \( i \) is the monthly interest rate expressed as a decimal (0.005).

Plugging in the values:
\[ (1 + 0.005)^{6} - 1 \]

Calculating the values inside the parentheses first:
\[ 1.005^{6} \approx 1.030378 \]

Now:
\[ 1.030378 - 1 = 0.030378 \]

Therefore, the equivalent semiannual interest rate is approximately **3.0378%**.

Would you like any further details or explanations on this solution? Here are five more questions you might find interesting:

1. How would you convert an annual interest rate to a quarterly equivalent?
2. What is the effective annual rate for an interest rate compounded monthly?
3. How do you calculate the future value of an annuity with quarterly payments?
4. What impact does compounding frequency have on the present value of an annuity?
5. How can you determine the nominal interest rate from the effective interest rate?

**Tip:** Understanding how to convert interest rates between different compounding periods is essential for accurate financial planning and comparison of investment options.

Learn how to calculate the equivalent periodic interest rate per payment interval for an annuity with semiannual payments earning 6% compounded monthly. This problem involves compound interest and annuities, including monthly interest rate calculation and conversion formula for interest rates between compounding periods. Suitable for advanced high school students or undergraduate level.

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