For the given corporate​ bond, whose annual simple interest rate is​ provided, find the semiannual simple interest payment and the total interest earned over the life of the bond. Assume 365 days in a year.
​$5700
 
Company Upper A
​, 
​30-year bond, 5.814
​%


To solve this problem, we'll follow these steps:

1. **Find the semiannual simple interest payment:**
   - The bond has a face value of $5700, an annual simple interest rate of 5.814%, and interest is paid semiannually (every 6 months).
   - The formula for simple interest is:

   \[
   I = P \times r \times t
   \]

   where:
   - $ I $ is the interest,
   - $ P $ is the principal amount,
   - $ r $ is the interest rate per period,
   - $ t $ is the time period (in years).

   Since interest is paid semiannually, $ t = \frac{1}{2} $ (6 months) and the rate per 6 months is $ r = \frac{5.814\%}{2} $.

   2. **Find the total interest earned over 30 years:**
   - For the total interest, we will compute the interest paid over all periods. Since the bond lasts for 30 years, there will be $ 2 \times 30 = 60 $ semiannual payments.

### Step 1: Calculate the semiannual simple interest payment
The semiannual interest rate is $ \frac{5.814\%}{2} = 2.907\% $.

The semiannual interest payment is:

\[
I_{\text{semiannual}} = 5700 \times \frac{2.907}{100} = 5700 \times 0.02907
\]

\[
I_{\text{semiannual}} = 165.699
\]

So, the semiannual simple interest payment is **$165.70** (rounded to 2 decimal places).

### Step 2: Calculate the total interest earned over the life of the bond
Over the 30 years, there are 60 semiannual periods. The total interest is:

\[
I_{\text{total}} = 165.70 \times 60
\]

\[
I_{\text{total}} = 9942.00
\]

So, the total interest earned over the life of the bond is **$9,942.00**.

---

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the total interest change if the bond had a different interest rate?
2. What if interest is compounded instead of being paid simply?
3. How does the number of years affect the total interest earned?
4. What happens if the bond value is different (e.g., $10,000)?
5. How would changing the frequency of payments (e.g., quarterly) affect the interest?

**Tip:** When calculating interest over long periods, it's crucial to distinguish between simple and compound interest, as compound interest grows faster.

For the given corporate bond, whose annual simple interest rate is provided, find the semiannual simple interest payment and the total interest earned over the life of the bond. Assume 365 days in a year. $5700 Company Upper A, 30-year bond, 5.814%.

Learn how to calculate the semiannual simple interest and total interest earned on a $5700 bond over 30 years with a 5.814% annual simple interest rate. This problem involves key financial math concepts such as simple interest and interest rate per period.

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