Let's break down the **accrued interest** calculation step by step. ### **Given:** - **Coupon rate:** 4% per year - **Coupon payment:** Semi-annual (twice a year) - **Face value:** 100 - **Day count convention:** 30/360 - **Maturity date:** 8/15/20 - **Settlement date (today):** 12/10/19 --- ## **Step 1: Calculate the semi-annual coupon payment** \[ \text{Coupon payment per period} = \frac{4\% \times 100}{2} = 2.00 \] --- ## **Step 2: Find the last coupon payment date** Coupons are paid semi-annually. Let’s assume standard payment dates: **2/15** and **8/15** each year. - The last coupon before 12/10/19 = **8/15/19** - The next coupon = **2/15/20** --- ## **Step 3: Calculate number of days from last coupon to settlement (accrual period)** **Day count convention:** 30/360 - **Last coupon date:** 8/15/19 - **Settlement date:** 12/10/19 ### **Months:** - From 8/15/19 to 12/10/19 - August 15 to December 10 = August, September, October, November, December Now, using 30/360, the formula for days between two dates: \[ \text{Number of days} = 360 \times (Y_2 - Y_1) + 30 \times (M_2 - M_1) + (D_2 - D_1) \] Where: - Last coupon: Y1 = 2019, M1 = 8, D1 = 15 - Settlement: Y2 = 2019, M2 = 12, D2 = 10 So, \[ \text{Days} = 360 \times (2019 - 2019) + 30 \times (12 - 8) + (10 - 15) \] \[ = 0 + 30 \times 4 + (-5) \] \[ = 120 - 5 = 115 \text{ days} \] --- ## **Step 4: Calculate accrued interest** Each period is **180 days** (6 months × 30 days/month). \[ \text{Accrued Interest} = \text{Coupon Payment} \times \frac{\text{Number of days accrued}}{\text{Number of days in period}} \] \[ = 2.00 \times \frac{115}{180} \] \[ = 2.00 \times 0.638888... \] \[ = 1.2778 \] **Rounded to four decimals:** \[ \boxed{1.2778} \] --- ## **Final Answer** **The accrued interest on the bond as of 12/10/19 is:** \[ \boxed{1.2778} \] If you need the dirty price as well, let me know!