A five-year bond with a $1 000 face value has a yield to maturity of 5.5% and its coupon rate is 6.0% paid annually. The dirty price of this bond exactly six months after its second coupon payment is closest to:

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The dirty price of a bond includes the accrued interest since the last coupon payment in addition to the clean price (the present value of its future cash flows). To calculate the dirty price, we first find the clean price by discounting the future cash flows (annual coupon payments and the face value at maturity) at the bond's yield to maturity, and then add the accrued interest for the period since the last coupon payment.1. Calculate the clean price:- The annual coupon payment is 6% of $1,000 = $60.- There are 3.5 years left until maturity (since we're exactly six months after the second coupon payment of a five-year bond).- The present value of the coupon payments and the face value can be calculated using the formula for the present value of an annuity and the present value of a lump sum, respectively, both discounted at the yield to maturity of 5.5%.$$ \text{Clean Price} = \frac{60}{0.055} \left(1 - \frac{1}{(1 + 0.055)^{3.5}}\right) + \frac{1000}{(1 + 0.055)^{3.5}} $$2. Calculate the accrued interest:- Since the bond pays annually and we're calculating the price six months after the last coupon payment, the accrued interest is for half a year.- The accrued interest = $60 \times \frac{6}{12} = $30.3. Calculate the dirty price:- Add the accrued interest to the clean price.Given the options provided and the method of calculation, the correct answer is closest to $1,043.49, which includes both the present value of the bond's future cash flows and the accrued interest for the six months following the last coupon payment.

A Five-Year Bond with a $1 000 Face Value Has