Question

An Apple annual coupon bond has a coupon rate of 5.9%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 5.9%, 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 @5.9%	Disc CF	Weight	Wt * Year
1	$      59.00	0.9443	$   55.71	0.0557	0.06
2	$      59.00	0.8917	$   52.61	0.0526	0.11
3	$      59.00	0.8420	$   49.68	0.0497	0.15
4	$      59.00	0.7951	$   46.91	0.0469	0.19
4	$ 1,000.00	0.7951	$ 795.09	0.7951	3.18
Duration					3.68

Modified duration = Duration / [ 1 + YTM ]

= 3.68 / [ 1 + 0.059 ]

= 3.68 / 1.059

= 3.473

it specifies 1% change in YTM leads to 3.473% change in price of Bond.