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.