1. **Problem statement:** We have a 10-year bond with a face value of 1000, an 8.6% annual coupon rate paid semi-annually, and a current price of 1035.44. We want to find the bond's yield to maturity (YTM) expressed as an APR with semi-annual compounding. 2. **Identify known values:** - Face value (F) = 1000 - Coupon rate = 8.6% annually - Coupon payment per period (C) = $1000 \times \frac{8.6\%}{2} = 1000 \times 0.043 = 43$ - Number of periods (N) = 10 years \times 2 = 20 - Current price (P) = 1035.44 3. **Yield to maturity definition:** The price of the bond equals the present value of all future coupon payments plus the present value of the face value at maturity, discounted at the YTM rate per period $r$: $$ P = \sum_{t=1}^{N} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^N} $$ 4. **Calculate YTM:** We need to find $r$ such that: $$ 1035.44 = 43 \times \frac{1 - (1+r)^{-20}}{r} + \frac{1000}{(1+r)^{20}} $$ This equation cannot be solved algebraically, so we use numerical methods (e.g., trial and error, financial calculator, or Excel). 5. **Approximate YTM:** Using a financial calculator or Excel RATE function: - N = 20 - PMT = 43 - PV = -1035.44 (cash outflow) - FV = 1000 The semi-annual yield $r \approx 0.041$ (4.1%). 6. **Convert to APR:** Since YTM is semi-annual, APR = $r \times 2 = 4.1\% \times 2 = 8.20\%$. **Final answer:** The bond's yield to maturity is approximately **8.20% APR with semi-annual compounding**.