Question

{Continuation of Previous Question} Bond J is a 3 percent coupon bond. Bond K is a 9 percent coupon bond. Both bonds have 7 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 5 percent, Bond K will decrease in price by ……………………. percent (enter 5.5% as 5.5 not 0.055, min 2 decimal accuracy)

Answer 1

Duration of bond K is:

Period (in years)	Payment	Factor at 6%	Present value	Duration
(a)	(b)	(c)	(d): (b) × (c)	(a) × (d)
0.50	$              45.00	0.970873786	$              43.69	$                21.84
1.00	$              45.00	0.942595909	$              42.42	$                42.42
1.50	$              45.00	0.915141659	$              41.18	$                61.77
2.00	$              45.00	0.888487048	$              39.98	$                79.96
2.50	$              45.00	0.862608784	$              38.82	$                97.04
3.00	$              45.00	0.837484257	$              37.69	$              113.06
3.50	$              45.00	0.813091511	$              36.59	$              128.06
4.00	$              45.00	0.789409234	$              35.52	$              142.09
4.50	$              45.00	0.766416732	$              34.49	$              155.20
5.00	$              45.00	0.744093915	$              33.48	$              167.42
5.50	$              45.00	0.722421277	$              32.51	$              178.80
6.00	$              45.00	0.70137988	$              31.56	$              189.37
6.50	$              45.00	0.68095134	$              30.64	$              199.18
7.00	$         1,045.00	0.661117806	$            690.87	$           4,836.08
			$         1,169.44	$           6,412.30
Macaulay duration=	6412.3/1169.44	5.4832

Decrease in price = 5.4832 * 5% = 27.42%

Answer is 27.42