Question

A bond with 30 years to maturity has a face value of $1,000. The bond pays an 8 percent semiannual coupon, and the bond has a 7 percent nominal yield to maturity. What is the price of the bond today? DO NOT USE EXCEL

Answer 1

Price of bond is the present value of cash flow from bond.
Present value of coupon			$     997.79
Present value of face value			$     126.93
Present value of cash flow			$ 1,124.72
So, price of bond is		$ 1,124.72
Working:
# 1	Semi annual coupon		=	1000*4%	=	40
# 2	Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.035)^-60)/0.035			i	3.50%
				=	24.94473			n	60
# 3	Present value of 1			=	(1+0.035)^-60
				=	0.126934
# 4	Present value of coupon			=	Coupon * Present value of annuity of 1
				=	40.00	*	24.94473
				=	997.79
# 5	Present value of face value			=	Face value * present value of 1
				=	1000	*	0.126934
				=	126.93