Question

Find the duration of a 5.0% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 8.0%? Note: The face value of the bond is $100. (Do not round intermediate calculations. Round your answers to 4 decimal places.) 6% YTM Years 8% YTM Years

Answer 1

Given face value = 100, coupon bond of 5%, period = 3 years.

21 22 22 2 29 30 31 sday of confon & Pule 24.037 Olign 23.112 0.110 09.00 Period - YTM=8% &TM=87 PV 0.5 0.9615 0.9255 0.1058 0-2017 0.0178 10.00 11.00 12.00 TR < 18.452204 01.00 0.8889 22.222 0.3547 21.367 0.8218 20.5 0.7801 1210-04 02.00 3 03.00 04.00 Pollice) operad 05.00 0.0572 - 06.00 05 07.00 - D. 203) 0.2445 Vibres 2 2.5 - 12-184

Case 1) when ytm = 6%

Bond duration =

Period	coupon	pv factor for ytm 6%	pv of coupon	pv/ price	(pv/price)*period
-0.5	25	0.9708	24.27	0.1107	0.055
-1	25	0.9426	23.56	0.1075	0.1075
-1.5	25	0.9151	22.88	0.1044	0.1566
-2	25	0.8884	22.21	0.1013	0.2026
-2.5	25	0.8625	21.56	0.0983	0.2457
-3	25+100(fv)	0.8374	104.675	0.4776	1.433
			219.15		2.20

Hence bond duration = 2.2 years.

Case 2)

Similarly bond duration for ytm = 8% is 2.184 years. Detailed calculations in the attached.