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

Step 1: Calculate the semi-annual coupon payment.
The bond has a fixed coupon rate of 1% per annum, paid semi-annually. So, the semi-annual coupon payment is 1% / 2 = 0.5% of the face value.
Coupon payment = 0.5% * $100 = $0.5

Step 2: Calculate the semi-annual yield-to-maturity (YTM).
The bond's YTM is given as an annualised percentage rate (APR) compounding semi-annually. So, the semi-annual YTM is 3% / 2 = 1.5%.

Step 3: Calculate the present value of the coupon payments.
The bond will make 8 * 2 = 16 coupon payments over its life. The present value of these payments is the sum of the present value of each payment, discounted at the semi-annual YTM.
PV of coupon payments = $0.5 / (1 + 1.5%) + $0.5 / (1 + 1.5%)^2 + ... + $0.5 / (1 + 1.5%)^16

Step 4: Calculate the present value of the face value payment.
The bond will pay its face value at maturity. The present value of this payment is the face value discounted at the semi-annual YTM.
PV of face value = $100 / (1 + 1.5%)^16

Step 5: Add the present value of the coupon payments and the face value payment to get the bond price.
Bond price = PV of coupon payments + PV of face value

Using a financial calculator or spreadsheet software to do the calculations, the bond price comes out to be approximately $85.868736. So, the correct answer is e. $85.868736.

Question

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

Step 1: Calculate the semi-annual coupon payment. 
The bond has a fixed coupon rate of 1% per annum, paid semi-annually. So, the semi-annual coupon payment is 1% / 2 = 0.5% of the face value. 
Coupon payment = 0.5% * $100 = $0.5

Step 2: Calculate the semi-annual yield-to-maturity (YTM). 
The bond's YTM is given as an annualised percentage rate (APR) compounding semi-annually. So, the semi-annual YTM is 3% / 2 = 1.5%.

Step 3: Calculate the present value of the coupon payments. 
The bond will make 8 * 2 = 16 coupon payments over its life. The present value of these payments is the sum of the present value of each payment, discounted at the semi-annual YTM. 
PV of coupon payments = $0.5 / (1 + 1.5%) + $0.5 / (1 + 1.5%)^2 + ... + $0.5 / (1 + 1.5%)^16

Step 4: Calculate the present value of the face value payment. 
The bond will pay its face value at maturity. The present value of this payment is the face value discounted at the semi-annual YTM. 
PV of face value = $100 / (1 + 1.5%)^16

Step 5: Add the present value of the coupon payments and the face value payment to get the bond price. 
Bond price = PV of coupon payments + PV of face value

Using a financial calculator or spreadsheet software to do the calculations, the bond price comes out to be approximately $85.868736. So, the correct answer is e. $85.868736.

Knowee AI · Accepted Answer

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

Step 1: Calculate the semi-annual coupon payment. 
The bond has a fixed coupon rate of 1% per annum, paid semi-annually. So, the semi-annual coupon payment is 1% / 2 = 0.5% of the face value. 
Coupon payment = 0.5% * $100 = $0.5

Step 2: Calculate the semi-annual yield-to-maturity (YTM). 
The bond's YTM is given as an annualised percentage rate (APR) compounding semi-annually. So, the semi-annual YTM is 3% / 2 = 1.5%.

Step 3: Calculate the present value of the coupon payments. 
The bond will make 8 * 2 = 16 coupon payments over its life. The present value of these payments is the sum of the present value of each payment, discounted at the semi-annual YTM. 
PV of coupon payments = $0.5 / (1 + 1.5%) + $0.5 / (1 + 1.5%)^2 + ... + $0.5 / (1 + 1.5%)^16

Step 4: Calculate the present value of the face value payment. 
The bond will pay its face value at maturity. The present value of this payment is the face value discounted at the semi-annual YTM. 
PV of face value = $100 / (1 + 1.5%)^16

Step 5: Add the present value of the coupon payments and the face value payment to get the bond price. 
Bond price = PV of coupon payments + PV of face value

Using a financial calculator or spreadsheet software to do the calculations, the bond price comes out to be approximately $85.868736. So, the correct answer is e. $85.868736.

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