To calculate the bond's clean price, 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 payment at maturity.

Here are the steps:

1. First, we need to calculate the semi-annual coupon payment. The bond pays 8% per year, so the semi-annual coupon payment is 8%/2 = 4% of the face value. That's $100 * 4% = $4.

2. Next, we need to calculate the semi-annual yield to maturity. The bond's yield to maturity is 10% per year, so the semi-annual yield to maturity is 10%/2 = 5%.

3. Now, we can calculate the present value of the bond's future cash flows. The bond has 19 months to maturity, which is about 1.58 years, or approximately 3 semi-annual periods.

The present value of the coupon payments is $4 / (1+5%) + $4 / (1+5%)^2 + $4 / (1+5%)^3 = $3.81 + $3.63 + $3.46 = $10.90.

The present value of the face value payment at maturity is $100 / (1+5%)^3 = $86.38.

4. Finally, we add up the present values of the future cash flows to get the bond's clean price. That's $10.90 + $86.38 = $97.28.

So, the closest answer is C. $97.12.

Question

To calculate the bond's clean price, 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 payment at maturity.

Here are the steps:

1. First, we need to calculate the semi-annual coupon payment. The bond pays 8% per year, so the semi-annual coupon payment is 8%/2 = 4% of the face value. That's $100 * 4% = $4.

2. Next, we need to calculate the semi-annual yield to maturity. The bond's yield to maturity is 10% per year, so the semi-annual yield to maturity is 10%/2 = 5%.

3. Now, we can calculate the present value of the bond's future cash flows. The bond has 19 months to maturity, which is about 1.58 years, or approximately 3 semi-annual periods.

The present value of the coupon payments is $4 / (1+5%) + $4 / (1+5%)^2 + $4 / (1+5%)^3 = $3.81 + $3.63 + $3.46 = $10.90.

The present value of the face value payment at maturity is $100 / (1+5%)^3 = $86.38.

4. Finally, we add up the present values of the future cash flows to get the bond's clean price. That's $10.90 + $86.38 = $97.28.

So, the closest answer is C. $97.12.

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, which include the semi-annual coupon payments and the face value payment at maturity.

Here are the steps:

1. First, we need to calculate the semi-annual coupon payment. The bond pays 8% per year, so the semi-annual coupon payment is 8%/2 = 4% of the face value. That's $100 * 4% = $4.

2. Next, we need to calculate the semi-annual yield to maturity. The bond's yield to maturity is 10% per year, so the semi-annual yield to maturity is 10%/2 = 5%.

3. Now, we can calculate the present value of the bond's future cash flows. The bond has 19 months to maturity, which is about 1.58 years, or approximately 3 semi-annual periods.

The present value of the coupon payments is $4 / (1+5%) + $4 / (1+5%)^2 + $4 / (1+5%)^3 = $3.81 + $3.63 + $3.46 = $10.90.

The present value of the face value payment at maturity is $100 / (1+5%)^3 = $86.38.

4. Finally, we add up the present values of the future cash flows to get the bond's clean price. That's $10.90 + $86.38 = $97.28.

So, the closest answer is C. $97.12.

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. $98.89 C. $97.12 D. $96.84

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