To calculate the bond's clean price, we need to calculate the present value of the bond's future cash flows, discounted at the yield to maturity rate.

Step 1: Calculate the semi-annual coupon payment
The bond pays an 8% coupon annually, so the semi-annual coupon payment is 4% of the face value, or $4.

Step 2: Calculate the number of periods until maturity
The bond has 19 months to maturity, which is approximately 1.58 years. Since coupons are paid semi-annually, there are approximately 3.16 periods until maturity. We'll round this to 3 periods for simplicity.

Step 3: Calculate the present value of the coupon payments
The present value of the coupon payments is the sum of the present values of each individual payment. The present value of a payment is calculated as Payment / (1 + r)^n, where r is the yield to maturity rate and n is the number of periods until the payment is made.

PV_Coupon = $4 / (1 + 0.10/2) + $4 / (1 + 0.10/2)^2 + $4 / (1 + 0.10/2)^3 = $3.64 + $3.31 + $3.01 = $9.96

Step 4: Calculate the present value of the face value
The present value of the face value is calculated in the same way as the present value of the coupon payments, but n is the number of periods until the bond matures.

PV_Face Value = $100 / (1 + 0.10/2)^3 = $86.38

Step 5: Add the present value of the coupon payments and the face value to get the bond's clean price
Clean Price = PV_Coupon + PV_Face Value = $9.96 + $86.38 = $96.34

So, the closest answer is C. $96.84.

Question

To calculate the bond's clean price, we need to calculate the present value of the bond's future cash flows, discounted at the yield to maturity rate.

Step 1: Calculate the semi-annual coupon payment
The bond pays an 8% coupon annually, so the semi-annual coupon payment is 4% of the face value, or $4.

Step 2: Calculate the number of periods until maturity
The bond has 19 months to maturity, which is approximately 1.58 years. Since coupons are paid semi-annually, there are approximately 3.16 periods until maturity. We'll round this to 3 periods for simplicity.

Step 3: Calculate the present value of the coupon payments
The present value of the coupon payments is the sum of the present values of each individual payment. The present value of a payment is calculated as Payment / (1 + r)^n, where r is the yield to maturity rate and n is the number of periods until the payment is made.

PV_Coupon = $4 / (1 + 0.10/2) + $4 / (1 + 0.10/2)^2 + $4 / (1 + 0.10/2)^3 = $3.64 + $3.31 + $3.01 = $9.96

Step 4: Calculate the present value of the face value
The present value of the face value is calculated in the same way as the present value of the coupon payments, but n is the number of periods until the bond matures.

PV_Face Value = $100 / (1 + 0.10/2)^3 = $86.38

Step 5: Add the present value of the coupon payments and the face value to get the bond's clean price
Clean Price = PV_Coupon + PV_Face Value = $9.96 + $86.38 = $96.34

So, the closest answer is C. $96.84.

Knowee AI · Accepted Answer

To calculate the bond's clean price, we need to calculate the present value of the bond's future cash flows, discounted at the yield to maturity rate.

Step 1: Calculate the semi-annual coupon payment
The bond pays an 8% coupon annually, so the semi-annual coupon payment is 4% of the face value, or $4.

Step 2: Calculate the number of periods until maturity
The bond has 19 months to maturity, which is approximately 1.58 years. Since coupons are paid semi-annually, there are approximately 3.16 periods until maturity. We'll round this to 3 periods for simplicity.

Step 3: Calculate the present value of the coupon payments
The present value of the coupon payments is the sum of the present values of each individual payment. The present value of a payment is calculated as Payment / (1 + r)^n, where r is the yield to maturity rate and n is the number of periods until the payment is made.

PV_Coupon = $4 / (1 + 0.10/2) + $4 / (1 + 0.10/2)^2 + $4 / (1 + 0.10/2)^3 = $3.64 + $3.31 + $3.01 = $9.96

Step 4: Calculate the present value of the face value
The present value of the face value is calculated in the same way as the present value of the coupon payments, but n is the number of periods until the bond matures.

PV_Face Value = $100 / (1 + 0.10/2)^3 = $86.38

Step 5: Add the present value of the coupon payments and the face value to get the bond's clean price
Clean Price = PV_Coupon + PV_Face Value = $9.96 + $86.38 = $96.34

So, the closest answer is C. $96.84.

An 8% coupon-paying bond has a yield to maturity of 10% p.a. The bond has a face value of $100 and 19 months to maturity. Coupons are paid semi-annually. What is the bond’s clean price? Choose the closest answer. A. $100 B. $97.12 C. $96.84 D. $98.89

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