Here’s how to solve the bond price calculation in **2 steps**: --- ### **Step 1: Identify Cash Flows and Market Rate** - **Face value of bonds:** $540,000 - **Stated interest rate:** 10% (paid semiannually) - **Market interest rate:** 12% (paid semiannually) - **Interest payment:** $540,000 × 10% × 1/2 = $27,000 every 6 months - **Number of periods:** 10 years × 2 = 20 periods #### **Explanation:** We break the total interest into semiannual periods because interest is paid twice a year. The market rate is also adjusted to a semiannual rate (12% / 2 = 6%). --- ### **Step 2: Calculate Present Value of Cash Flows** - **Present Value of Interest Payments (Annuity):** \[ PV_{\text{interest}} = \text{PMT} \times PV_{\text{annuity}}(n=20, r=6\%) \] \[ PV_{\text{interest}} = \$27,000 \times 11.46992 = \$309,687.84 \] (Using PV factor for 20 periods at 6%) - **Present Value of Principal (Single Sum):** \[ PV_{\text{principal}} = FV \times PV_{\text{single sum}}(n=20, r=6\%) \] \[ PV_{\text{principal}} = \$540,000 \times .3118 = \$168,372 \] - **Total Present Value (Issue Price):** \[ PV_{\text{total}} = PV_{\text{interest}} + PV_{\text{principal}} \] \[ PV_{\text{total}} = \$309,687.84 + \$168,372 = \$478,059.84 \] #### **Explanation:** We use present value formulas for both the annuity (semiannual interest payments) and the lump sum (principal at maturity), both discounted at the market rate. --- ## **Final Answer** **The price of the bonds on January 1, 2021, is \$478,060 (rounded to the nearest dollar).**