A 4% coupon-paying bond with two years’ life has a yield to maturity of 7% p.a with face valueof 100 and provides semi-annual payment.The bond’s dirty price is and clean price is under when the bond still has 20months to maturity.A. $96.6825; $95.8234B. $94.4904; $95.8234C. $94.4904; $96.6825D. $96.6825; $95.3492E. None of these are correct

Let's break this down step by step:

1. We're talking about a coupon-paying bond. This is a type of bond where you get interest payments (called coupons) regularly. It's like buying a toy for $10 and then getting$1 back every month for the next 10 months.

2. The bond has a face value of $100. This is the amount you'll get when the bond matures. It's like the$10 you paid for the toy.

3. The bond matures in 2 years. This is how long you have to wait before you can sell the bond (or toy) and get the face value.

4. The bond's coupon rate is 4% per year, and it provides semi-annual payments. This means you get 2% of the face value every 6 months. It's like getting $0.50 back every 6 months for the$10 toy you bought.

5. The bond's yield to maturity is 7% per year. This is the total return you'll get if you hold the bond until it matures, including both the coupons and the face value. It's like saying if you put your money in a bank instead of buying the bond, the bank would give you a 7% return on your money every year.

Now, we need to find the dirty price and clean price of the bond.

The dirty price is the total amount you need to pay to buy the bond, including any interest that has accrued since the last coupon payment. It's like the total price you pay for the toy, including any sales tax.

The clean price is the dirty price minus the accrued interest. It's like the price of the toy without the sales tax.

To calculate the dirty price, we use the formula for the present value of a bond, which is:

Dirty Price = (Coupon / (1 + Yield/2)) + (Coupon / (1 + Yield/2)^2) + ... + (Coupon + Face Value) / (1 + Yield/2)^n

where n is the number of periods until maturity.

So, if we plug in the numbers:

Dirty Price = ($2 / (1 + 0.07/2)) + ($2 / (1 + 0.07/2)^2) + ($2 / (1 + 0.07/2)^3) + ($102 / (1 + 0.07/2)^4) = $94.4904

So, the dirty price of the bond is $94.4904.

To calculate the clean price, we subtract the accrued interest from the dirty price. The accrued interest is the amount of the next coupon payment that has been earned but not yet paid. Since the bond still has 20 months to maturity, 2 months of interest has accrued. This is:

Accrued Interest = Coupon * (2 / 6) = $2 * (2 / 6) =$0.6667

So, the clean price is:

Clean Price = Dirty Price - Accrued Interest = $94.4904 -$0.6667 = $93.8237

So, the correct answer is not listed among the options. The correct values would be Dirty Price: $94.4904 and Clean Price:$93.8237.

To answer this question, we first need to understand the terms used:

1. Coupon-paying bond: This is a bond that pays interest to its holder periodically before the bond's maturity date.
2. Yield to maturity (YTM): This is the total return anticipated on a bond if it is held until it matures.
3. Dirty price: This is the price of a bond including accrued interest.
4. Clean price: This is the price of a bond excluding accrued interest.

Now, let's calculate the dirty price and clean price of the bond:

Step 1: Calculate the semi-annual coupon payment The bond has a 4% annual coupon rate, so the semi-annual coupon payment is 4%/2 = 2% of the face value. Therefore, the semi-annual coupon payment is 2% * $100 =$2.

Step 2: Calculate the present value of the coupon payments The bond has 2 years to maturity and pays semi-annually, so there are 2*2 = 4 periods. The present value of the coupon payments is the sum of the present values of each coupon payment. The present value of a payment is the payment divided by (1 + YTM/2) to the power of the period. The YTM is 7%, so the semi-annual YTM is 7%/2 = 3.5%.

PV_coupon = $2/(1+3.5$2/(1+3.5%)^2 + $2/(1+3.5$2/(1+3.5%)^4 = $1.9324 +$1.8671 + $1.8037 +$1.7423 = $7.3455

Step 3: Calculate the present value of the face value The present value of the face value is the face value divided by (1 + YTM/2) to the power of the number of periods.

PV_face value = $100/(1+3.5$89.3370

Step 4: Calculate the dirty price The dirty price is the sum of the present value of the coupon payments and the present value of the face value.

Dirty price = PV_coupon + PV_face value = $7.3455 +$89.3370 = $96.6825

Step 5: Calculate the clean price The clean price is the dirty price minus the accrued interest. The accrued interest is the coupon payment times the fraction of the coupon period that has passed. There are 20 months to maturity, so the fraction of the coupon period that has passed is (6-20%6)/6 = 1/3.

Accrued interest = $2 * 1/3 =$0.6667

Clean price = Dirty price - Accrued interest = $96.6825 -$0.6667 = $96.0158

Therefore, the answer is E. None of these are correct. The dirty price is $96.6825 and the clean price is$96.0158.