1. **State the problem:** We have a bond with a par value of 1000, 10 years to maturity, a 7% annual coupon, and a current price of 985. We need to find its yield to maturity (YTM) and then find the price 3 years from today assuming the YTM remains constant. 2. **Formula for Yield to Maturity (YTM):** The price of a bond is the present value of its future cash flows: $$\text{Price} = \sum_{t=1}^{N} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^N}$$ where: - $C$ = annual coupon payment = $1000 \times 0.07 = 70$ - $F$ = face value = 1000 - $N$ = number of years to maturity = 10 - $y$ = yield to maturity (annual) 3. **Calculate YTM:** We solve for $y$ in: $$985 = \sum_{t=1}^{10} \frac{70}{(1+y)^t} + \frac{1000}{(1+y)^{10}}$$ This requires iterative methods or a financial calculator. Using approximation or a financial calculator, the YTM is approximately 7.15%. 4. **Price 3 years from today:** After 3 years, the bond will have $10 - 3 = 7$ years left to maturity. The price then is: $$P_3 = \sum_{t=1}^{7} \frac{70}{(1+0.0715)^t} + \frac{1000}{(1+0.0715)^7}$$ Calculating each term: - Present value of coupons: $$PV_{coupons} = 70 \times \frac{1 - (1+0.0715)^{-7}}{0.0715} \approx 70 \times 5.389 = 377.23$$ - Present value of face value: $$PV_{face} = \frac{1000}{(1.0715)^7} \approx \frac{1000}{1.713} = 583.99$$ 5. **Sum to find price:** $$P_3 = 377.23 + 583.99 = 961.22$$ **Final answers:** - Yield to maturity $\approx 7.15\%$ - Price 3 years from today $\approx 961.22$