Question

What is the price (p) and duration (d) of a 6% coupon bond maturing in 20 years and paying interst annually if the current interest rate is 9%?

Select one:

A) p= 311.80, d= 9.18

B) p= 726.14, d= 10.77

C) p= 726.14, d= 11.55

D) p= 1,344.10, d= 12.43

Answer 1

Ans: B)p= 726.14, d= 10.77

Let the Face value of the bond be 1000. The coupon payment =1000*0.06=60

Price of a bond = Sum of PV of future cash flows

= Interest*PVAF(9%,20years) + Face value*PVAF(9%,20years)

=(60*9.1285)+(1000*.1784) =$726.14

Duration of a bond calculation:

Period	Cash Flow	Period x cash flow	PVF @ 9%	PV of cash Flow
1	60	60	0.9174	55.05
2	60	120	0.8417	101.00
3	60	180	0.7722	138.99
4	60	240	0.7084	170.02
5	60	300	0.6499	194.98
6	60	360	0.5963	214.66
7	60	420	0.5470	229.75
8	60	480	0.5019	240.90
9	60	540	0.4604	248.63
10	60	600	0.4224	253.45
11	60	660	0.3875	255.77
12	60	720	0.3555	255.99
13	60	780	0.3262	254.42
14	60	840	0.2992	251.37
15	60	900	0.2745	247.08
16	60	960	0.2519	241.79
17	60	1020	0.2311	235.69
18	60	1080	0.2120	228.95
19	60	1140	0.1945	221.72
20	1060	21200	0.1784	3,782.73
			Total	7,822.95

Duration of bond = sum of weighted average cash flows of the bond/ current price of the bond

=7822.95/726.14 = 10.77