To calculate the market price of the bond, we need to calculate the present value of the bond's future cash flows, which consist of semiannual coupon payments and the face value payment at maturity.

Here are the steps:

1. First, we need to calculate the semiannual coupon payment. The bond has a coupon rate of 5.76 percent, and it pays semiannually, so each payment is (5.76/2)% of the par value. That's (5.76/2)/100 * $1,000 = $28.8.

2. Next, we need to calculate the present value of these semiannual payments. There are 21 years left until maturity, and since the bond pays semiannually, that's 21*2 = 42 periods. The yield to maturity is 6.3 percent per year, but since payments are semiannual, we need to use a semiannual discount rate, which is (6.3/2)% = 3.15%. The present value of the coupon payments is $28.8 * (1 - (1 + 3.15/100)^-42) / (3.15/100) = $28.8 * 21.999 = $634.77.

3. We also need to calculate the present value of the face value payment at maturity. The face value is $1,000, and we need to discount it back 42 periods at a semiannual rate of 3.15%. The present value of the face value is $1,000 / (1 + 3.15/100)^42 = $1,000 / 3.39 = $294.98.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the market price of the bond. The market price is $634.77 + $294.98 = $929.75.

So, the market price of the bond is approximately $929.75.

Question

To calculate the market price of the bond, we need to calculate the present value of the bond's future cash flows, which consist of semiannual coupon payments and the face value payment at maturity.

Here are the steps:

1. First, we need to calculate the semiannual coupon payment. The bond has a coupon rate of 5.76 percent, and it pays semiannually, so each payment is (5.76/2)% of the par value. That's (5.76/2)/100 * $1,000 = $28.8.

2. Next, we need to calculate the present value of these semiannual payments. There are 21 years left until maturity, and since the bond pays semiannually, that's 21*2 = 42 periods. The yield to maturity is 6.3 percent per year, but since payments are semiannual, we need to use a semiannual discount rate, which is (6.3/2)% = 3.15%. The present value of the coupon payments is $28.8 * (1 - (1 + 3.15/100)^-42) / (3.15/100) = $28.8 * 21.999 = $634.77.

3. We also need to calculate the present value of the face value payment at maturity. The face value is $1,000, and we need to discount it back 42 periods at a semiannual rate of 3.15%. The present value of the face value is $1,000 / (1 + 3.15/100)^42 = $1,000 / 3.39 = $294.98.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the market price of the bond. The market price is $634.77 + $294.98 = $929.75.

So, the market price of the bond is approximately $929.75.

Knowee AI · Accepted Answer

To calculate the market price of the bond, we need to calculate the present value of the bond's future cash flows, which consist of semiannual coupon payments and the face value payment at maturity.

Here are the steps:

1. First, we need to calculate the semiannual coupon payment. The bond has a coupon rate of 5.76 percent, and it pays semiannually, so each payment is (5.76/2)% of the par value. That's (5.76/2)/100 * $1,000 = $28.8.

2. Next, we need to calculate the present value of these semiannual payments. There are 21 years left until maturity, and since the bond pays semiannually, that's 21*2 = 42 periods. The yield to maturity is 6.3 percent per year, but since payments are semiannual, we need to use a semiannual discount rate, which is (6.3/2)% = 3.15%. The present value of the coupon payments is $28.8 * (1 - (1 + 3.15/100)^-42) / (3.15/100) = $28.8 * 21.999 = $634.77.

3. We also need to calculate the present value of the face value payment at maturity. The face value is $1,000, and we need to discount it back 42 periods at a semiannual rate of 3.15%. The present value of the face value is $1,000 / (1 + 3.15/100)^42 = $1,000 / 3.39 = $294.98.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the market price of the bond. The market price is $634.77 + $294.98 = $929.75.

So, the market price of the bond is approximately $929.75.

Whatever, Incorporated, has a bond outstanding with a coupon rate of 5.76 percent and semiannual payments. The yield to maturity is 6.3 percent and the bond matures in 21 years. What is the market price if the bond has a par value of $1,000?

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