Question

A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a 7 percent promised YTM, and 10 years to maturity. Find the bond's duration.

Answer 1

Answer :

Calculation of Bond's Duration :

Below is the table showing calculation of Bond's Duration:

Year (Weights)	Cah Flows	PVF @3.5%	Discounted Cash Flows	Weights * Discounted Cash Flows
1	35	0.966183575	33.81642512	33.81642512
2	35	0.9335107	32.67287451	65.34574903
3	35	0.901942706	31.5679947	94.7039841
4	35	0.871442228	30.50047797	122.0019119
5	35	0.841973167	29.46906084	147.3453042
6	35	0.813500644	28.47252255	170.8351353
7	35	0.785990961	27.50968362	192.5677854
8	35	0.759411556	26.57940447	212.6352357
9	35	0.733730972	25.68058403	231.1252562
10	35	0.708918814	24.81215848	248.1215848
11	35	0.684945714	23.97309998	263.7040998
12	35	0.661783298	23.16241544	277.9489853
13	35	0.639404153	22.37914535	290.9288896
14	35	0.61778179	21.62236266	302.7130772
15	35	0.596890619	20.89117165	313.3675748
16	35	0.576705912	20.18470691	322.9553106
17	35	0.557203779	19.50213228	331.5362488
18	35	0.53836114	18.84263988	339.1675179
19	35	0.52015569	18.20544916	345.9035341
20	1035	0.502565884	520.1556904	10403.11381
		Total	1000	14709.83742

Coupon Payment in every six month = 1000 * 7%/2 = 35

Years to maturity = 10 * 2 = 20 (Multiplied by 2 as semi annual coupon payment)

Yield to maturity = 7% / 2 = 3.5%

Duration = [Sum of (Weights * Discounted Cash Flows)] / Discounted Cash Flows

= 14,709.83742 / 1000

= 14.70983742 half years or 7.354918709 years or 7.35 years.