Question

An Apple annual coupon bond has a coupon rate of 4.1%, face value of $1,000, and 4 years to maturity. If its yield to maturity is 4.1%, what is its Modified Duration? Answer in years, rounded to three decimal places.

Answer 1

Modified duration is 3.622 Years

Step-1:Calculation of macualay duration
Macualay duration		=	Sum of weighted present value/Initial Price
		=	$   3,769.83	/	$ 1,000.00
		=	3.770
Year	Cash flow	Weighted Cash	Discount factor	Present value of weighted cash flow
a	b	c=a*b	d=1.041^-a	e=c*d
1	$       41.00	$       41.00	0.9606	$         39.39
2	$       41.00	$       82.00	0.9228	$         75.67
3	$       41.00	$     123.00	0.8864	$       109.03
4	$ 1,041.00	$ 4,164.00	0.8515	$   3,545.75
Total				$   3,769.83
Step-2:Calculation of modified duration
Modified duration		=	Macaulay duration/(1+i)
		=	3.770/(1+0.041)
		=	3.622