Answer: $1,043.76, $1,028.76

To calculate the dirty and clean prices: **Given:** - Face value = $1,000 - Coupon rate = 6% (semiannual) - Semiannual coupon = $1,000 × 6%/2 = $30 - Remaining coupon payments = 10 - Market rate = 5% (semiannual) - Semiannual market rate = 5%/2 = 2.5% - Days to next coupon = 90 - Days in coupon period = 180 (assuming 30/360 convention) **Step 1: Calculate dirty price (full price)** The dirty price is the present value of all future cash flows. Dirty Price = PV of coupons + PV of principal Using the bond pricing formula: Dirty Price = C × [1 - (1+r)^-n]/r + FV/(1+r)^n Where: - C = $30 - r = 2.5% - n = 10 - FV = $1,000 Dirty Price = 30 × [1 - (1.025)^-10]/0.025 + 1,000/(1.025)^10 First term: 30 × [1 - 1/1.280085]/0.025 = 30 × [1 - 0.781198]/0.025 = 30 × 0.218802/0.025 = 30 × 8.75208 = 262.562 Second term: 1,000/1.280085 = 781.198 Dirty Price = 262.562 + 781.198 = $1,043.76 **Step 2: Calculate accrued interest** Accrued Interest = Coupon × (Days since last coupon / Days in coupon period) = $30 × (90/180) = $30 × 0.5 = $15 **Step 3: Calculate clean price** Clean Price = Dirty Price - Accrued Interest = $1,043.76 - $15 = $1,028.76 Therefore, the dirty price is $1,043.76 and the clean price is $1,028.76.

Author: LeetQuiz Editorial Team