Question

An Apple annual coupon bond has a coupon rate of 6.9%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 6.9%, what is its Modified Duration? Answer in years, rounded to three decimal places.

Answer 1

Modified Duration = Duration / (1+YTM)

Duration = Sum [ Weight * Year ]

Year	CF	PVF @6.9%	Disc CF	Weight	Duration
1	$      69.00	0.9355	$   64.55	0.0645	0.06
2	$      69.00	0.8751	$   60.38	0.0604	0.12
3	$      69.00	0.8186	$   56.48	0.0565	0.17
4	$      69.00	0.7658	$   52.84	0.0528	0.21
4	$ 1,000.00	0.7658	$ 765.75	0.7658	3.06
Duration					3.63

Modfied duration = Duration / ( 1+YTM)

= 3.63 / ( 1 + 0.069)

= 3.63 / 1.069

= 3.40%

Modified duartion is 3.40%