1. **State the problem:** We have a 10-year bond with a face value of 1000, an 8.6% annual coupon rate paid semi-annually, currently priced at 1035.44. We want to find: a. The bond's yield to maturity (YTM) expressed as an APR with semi-annual compounding. b. The bond's price if the YTM changes to 9.8% APR. 2. **Given data:** - Face value (F) = 1000 - Coupon rate = 8.6% annually - Coupon payment frequency = semi-annual (2 times per year) - Number of years (N) = 10 - Current price (P) = 1035.44 - New YTM for part b = 9.8% APR 3. **Calculate coupon payment (C):** $$C = \frac{8.6\%}{2} \times 1000 = 0.043 \times 1000 = 43$$ 4. **Calculate total number of periods (n):** $$n = 10 \times 2 = 20$$ 5. **Part a: Find YTM (expressed as semi-annual rate r) such that:** $$P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$ We know P=1035.44, C=43, F=1000, n=20. We solve for $r$ numerically. Using a financial calculator or iterative method, the semi-annual yield $r \approx 0.0404$ (4.04%). 6. **Convert semi-annual yield to APR:** $$\text{YTM APR} = 2 \times r = 2 \times 0.0404 = 0.0808 = 8.08\%$$ 7. **Part b: Calculate new price if YTM changes to 9.8% APR:** New semi-annual yield: $$r_{new} = \frac{9.8\%}{2} = 0.049$$ Calculate new price: $$P_{new} = \sum_{t=1}^{20} \frac{43}{(1+0.049)^t} + \frac{1000}{(1+0.049)^{20}}$$ Calculate present value of coupons: $$PV_{coupons} = 43 \times \frac{1 - (1+0.049)^{-20}}{0.049} \approx 43 \times 12.4622 = 535.27$$ Calculate present value of face value: $$PV_{face} = \frac{1000}{(1+0.049)^{20}} \approx \frac{1000}{2.601} = 384.43$$ Sum to get new price: $$P_{new} = 535.27 + 384.43 = 919.70$$ **Final answers:** - a. Yield to maturity = 8.08% APR (semi-annual compounding) - b. New bond price if YTM = 9.8% APR is approximately 919.70