To find the new price and the percentage change for Betty's bond, let's break down the problem:

Given:

• Face value of bond = $100
• Coupon rate = 10% per annum, payable semiannually
• Yield to maturity decreases from 10% to 9% per annum, compounded semiannually.
• Bond term = 8 years
• Payments per year = 2 (semiannual payments)

Step 1: Semiannual coupon payment

The bond pays a coupon of 10% annually, so for semiannual payments: $\text{Coupon payment per period} = \frac{100 \times 10\%}{2} = 5 \, \text{dollars}$ Each payment period (which is every 6 months), the bondholder receives $5.

Step 2: Yield to maturity adjustment

The yield decreases from 10% per annum to 9% per annum compounded semiannually. Therefore, the semiannual yield is: $\text{Semiannual yield} = \frac{9\%}{2} = 4.5\%$

Step 3: Number of periods

Since the bond has a term of 8 years, with semiannual coupon payments: $\text{Number of periods} = 8 \times 2 = 16$

Step 4: Calculate the bond price using the new yield

The bond price can be calculated as the present value of future coupon payments and the face value of the bond, discounted at the new yield of 4.5% per period.

$\text{Bond price} = \sum_{t=1}^{16} \frac{5}{(1 + 0.045)^t} + \frac{100}{(1 + 0.045)^{16}}$

I will compute this sum for you now.The new price of the bond is approximately $105.62.

Step 5: Calculate the percentage change

The original bond price was $100. The percentage change is calculated as:

$\text{Percentage change} = \frac{\text{New price} - \text{Old price}}{\text{Old price}} \times 100 = \frac{105.62 - 100}{100} \times 100$

Let me compute that for you.The percentage change in the bond price is approximately 5.62%.

Final answers:

• New price: $105.62
• Percentage change: 5.62%

Would you like any more details or further clarification?

Here are 5 related questions to explore:

1. How does the bond price change if the yield increases instead of decreasing?
2. How do changes in coupon frequency affect bond prices?
3. What is the relationship between bond prices and interest rates?
4. How do you calculate the duration of a bond, and why is it important?
5. How would the price change if the bond was callable?

Tip: When bond yields decrease, bond prices rise because the fixed coupon payments become more attractive relative to the lower yield.