1. **Problem statement:** Calculate the value of a bond with face value Rs.1000, coupon rate 12%, maturity 7 years. 2. **Formula:** The value of a bond is the present value of its coupon payments plus the present value of the face value at maturity: $$\text{Bond Value} = \sum_{t=1}^n \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$$ where: - $C$ = annual coupon payment = $\text{Face Value} \times \text{Coupon Rate}$ - $F$ = face value - $r$ = discount rate (market interest rate) - $n$ = number of years to maturity 3. **Calculate coupon payment:** $$C = 1000 \times 0.12 = 120$$ 4. **(i) When discount rate $r=14\% = 0.14$:** Calculate present value of coupons: $$PV_{coupons} = 120 \times \sum_{t=1}^7 \frac{1}{(1.14)^t}$$ This is a geometric series with common ratio $\frac{1}{1.14}$. Sum of present value factors: $$S = \frac{1 - (1.14)^{-7}}{0.14} = \frac{1 - \frac{1}{(1.14)^7}}{0.14}$$ Calculate $(1.14)^7 \approx 2.5023$, so $$S = \frac{1 - \frac{1}{2.5023}}{0.14} = \frac{1 - 0.3996}{0.14} = \frac{0.6004}{0.14} = 4.2886$$ Therefore, $$PV_{coupons} = 120 \times 4.2886 = 514.63$$ Present value of face value: $$PV_{face} = \frac{1000}{(1.14)^7} = \frac{1000}{2.5023} = 399.6$$ Bond value: $$514.63 + 399.6 = 914.23$$ 5. **(ii) When discount rate $r=12\% = 0.12$:** Sum of present value factors: $$S = \frac{1 - (1.12)^{-7}}{0.12} = \frac{1 - \frac{1}{(1.12)^7}}{0.12}$$ Calculate $(1.12)^7 \approx 2.2107$, so $$S = \frac{1 - \frac{1}{2.2107}}{0.12} = \frac{1 - 0.4523}{0.12} = \frac{0.5477}{0.12} = 4.5642$$ Therefore, $$PV_{coupons} = 120 \times 4.5642 = 547.7$$ Present value of face value: $$PV_{face} = \frac{1000}{(1.12)^7} = \frac{1000}{2.2107} = 452.3$$ Bond value: $$547.7 + 452.3 = 1000$$ **Final answers:** (i) Bond value at 14% discount rate = Rs.914.23 (ii) Bond value at 12% discount rate = Rs.1000