Answer: $1,043.76, $1,028.76

## Explanation To calculate the dirty and clean prices of the bond: **Given:** - Par value = $1,000 - Coupon rate = 6% (semiannual = 3% per period) - Coupon payment = $1,000 × 3% = $30 - Market rate = 5% (semiannual = 2.5% per period) - Remaining payments = 10 - Days to next coupon = 90 - Total days in coupon period = 180 (assuming 30/360 convention) **Step 1: Calculate present value of remaining cash flows** Using the bond pricing formula: \[ \text{PV} = \sum_{t=1}^{10} \frac{30}{(1.025)^t} + \frac{1000}{(1.025)^{10}} \] This can be calculated as: - PV of coupons = 30 × [1 - (1.025)^{-10}] / 0.025 = 30 × 8.7521 = 262.56 - PV of principal = 1000 / (1.025)^{10} = 1000 / 1.2801 = 781.20 Total PV = 262.56 + 781.20 = $1,043.76 **Step 2: Calculate accrued interest** Accrued interest = Coupon payment × (Days elapsed / Total days) = $30 × (90 / 180) = $30 × 0.5 = $15 **Step 3: Calculate clean and dirty prices** - Dirty price = Present value = $1,043.76 - 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 .