Question

What is the duration of a $1,000 bond with 3 years to maturity and a coupon of 8% paid annually. Assume the investor’s discount rate is 6%? Show all calculations.

Answer 1

Period (in years)	Payment	Present value factor	Present value	Duration
(a)	(b)	(c)	(d): (b) × (c)	(a) × (d)
1.00	$      80.00	0.943396226	$      75.47	$      75.47
2.00	$      80.00	0.88999644	$      71.20	$    142.40
3.00	$ 1,080.00	0.839619283	$    906.79	$ 2,720.37
			$ 1,053.46	$ 2,938.24
Macaulay duration=	$2,938.24/ $1,053.46	2.79

Duration is 2.79 years

In year 1 and 2 interest paid at 8% on $1,000 is $80

In year 3 principal $1,000 and $80 interest payments add to $1,080

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