To calculate the fair value of the bond, we need to calculate the present value of the bond's future cash flows, which include the semi-annual coupon payments and the face value at maturity.

1. First, we need to calculate the semi-annual coupon payment. The bond pays a 3.40% annual coupon rate, semi-annually, so each payment is 3.40%/2 = 1.70% of the face value. Therefore, each coupon payment is $100 * 1.70% = $1.70.

2. Next, we need to calculate the present value of the coupon payments. There are 2 years until maturity and the bond pays semi-annually, so there are 2*2 = 4 payments. The present value of an annuity formula is C * [(1 - (1 + r)^-n) / r], where C is the coupon payment, r is the discount rate (current market yield divided by 2), and n is the number of periods. So, the present value of the coupon payments is $1.70 * [(1 - (1 + 6.45%/2)^-4) / (6.45%/2)] = $6.32.

3. We also need to calculate the present value of the face value, which is the amount the bondholder receives at maturity. The present value formula is FV / (1 + r)^n, where FV is the face value, r is the discount rate, and n is the number of periods. So, the present value of the face value is $100 / (1 + 6.45%/2)^4 = $87.87.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the fair value of the bond. So, the fair value of the bond is $6.32 + $87.87 = $94.19.

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To calculate the fair value of the bond, we need to calculate the present value of the bond's future cash flows, which include the semi-annual coupon payments and the face value at maturity.

1. First, we need to calculate the semi-annual coupon payment. The bond pays a 3.40% annual coupon rate, semi-annually, so each payment is 3.40%/2 = 1.70% of the face value. Therefore, each coupon payment is $100 * 1.70% = $1.70.

2. Next, we need to calculate the present value of the coupon payments. There are 2 years until maturity and the bond pays semi-annually, so there are 2*2 = 4 payments. The present value of an annuity formula is C * [(1 - (1 + r)^-n) / r], where C is the coupon payment, r is the discount rate (current market yield divided by 2), and n is the number of periods. So, the present value of the coupon payments is $1.70 * [(1 - (1 + 6.45%/2)^-4) / (6.45%/2)] = $6.32.

3. We also need to calculate the present value of the face value, which is the amount the bondholder receives at maturity. The present value formula is FV / (1 + r)^n, where FV is the face value, r is the discount rate, and n is the number of periods. So, the present value of the face value is $100 / (1 + 6.45%/2)^4 = $87.87.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the fair value of the bond. So, the fair value of the bond is $6.32 + $87.87 = $94.19.

Knowee AI · Accepted Answer

To calculate the fair value of the bond, we need to calculate the present value of the bond's future cash flows, which include the semi-annual coupon payments and the face value at maturity.

1. First, we need to calculate the semi-annual coupon payment. The bond pays a 3.40% annual coupon rate, semi-annually, so each payment is 3.40%/2 = 1.70% of the face value. Therefore, each coupon payment is $100 * 1.70% = $1.70.

2. Next, we need to calculate the present value of the coupon payments. There are 2 years until maturity and the bond pays semi-annually, so there are 2*2 = 4 payments. The present value of an annuity formula is C * [(1 - (1 + r)^-n) / r], where C is the coupon payment, r is the discount rate (current market yield divided by 2), and n is the number of periods. So, the present value of the coupon payments is $1.70 * [(1 - (1 + 6.45%/2)^-4) / (6.45%/2)] = $6.32.

3. We also need to calculate the present value of the face value, which is the amount the bondholder receives at maturity. The present value formula is FV / (1 + r)^n, where FV is the face value, r is the discount rate, and n is the number of periods. So, the present value of the face value is $100 / (1 + 6.45%/2)^4 = $87.87.

4. Finally, we add the present value of the coupon payments and the present value of the face value to get the fair value of the bond. So, the fair value of the bond is $6.32 + $87.87 = $94.19.

The following 3.40% p.a. semi-annual coupon U.S. treasury bond has 2 years until maturity. Calculate the fair value of the bond (rounded to 2 decimal places), assuming the current market yield for this bond is 6.45%. The bond has a face value of $100.00.

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