Question

An Apple annual coupon bond has a coupon rate of 7.6%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 7.6%, what is its Modified Duration? Answer in years, rounded to three decimal places.

Answer 1

Modified Duartion = Duration / (1+YTM)

Duration = Sum [ Weight * Year ]

Year	CF	PVF @7.6%	Disc CF	Weight	Duration
1	$      76.00	0.9294	$   70.63	0.0706	0.07
2	$      76.00	0.8637	$   65.64	0.0656	0.13
3	$      76.00	0.8027	$   61.01	0.0610	0.18
4	$      76.00	0.7460	$   56.70	0.0567	0.23
4	$ 1,000.00	0.7460	$ 746.02	0.7460	2.98
Duration					3.60

Modified Duration = Duration / (1+YTM)

= 3.60 / ( 1 + 0.0760)

= 3.6 / 1.076

= 3.346%