1. Problem statement: A bond with face value 1000 and coupon rate $12\%$ pays annual coupon payments and matures after 7 years. 2. We want the present value when the discount rate is $14\%$. 3. Formula used and rules: The present value of a bond equals the present value of the coupon annuity plus the present value of the face value. 4. Formula (display): $$PV = C \frac{1 - (1+r)^{-n}}{r} + FV(1+r)^{-n}$$ 5. Important rules: Coupons are treated as an ordinary annuity with payments at the end of each period. 6. Identify quantities: $C = 0.12 \times 1000 = 120$. 7. Set $r = 0.14$, $n = 7$, $FV = 1000$. 8. Compute $(1+r)^{n}$: $1.14^{7} = 2.502923171424$. 9. Compute discount factor: $(1+r)^{-n} = 2.502923171424^{-1} = 0.399531865$. 10. Present value of coupons: $$PV_{coupons} = 120 \cdot \frac{1 - (1.14)^{-7}}{0.14} = 120 \cdot \frac{1 - 0.399531865}{0.14} = 120 \cdot \frac{0.600468135}{0.14} = 120 \cdot 4.289058107 = 514.6869728$$ 11. Present value of face value: $$PV_{face} = 1000 \cdot (1.14)^{-7} = 1000 \cdot 0.399531865 = 399.531865$$ 12. Total present value: $$PV = 514.6869728 + 399.531865 = 914.2188378 \approx 914.22$$ 13. Final answer: The value of the bond at discount rate 14\% is approximately 914.22.