Question

Consider a three-year bond with 6% annual coupon (paid semi-annually). Suppose the yield on the bond is 8% per year with continuous compounding. What is the duration of the bond (in years)? (required precision: 0.01 +/- 0.01)

Answer 1

Following formula's are used to calculated duration of the bond;

Discount factor = e^(-0.08*t)

Face value = $1000

coupon = 3% of 1000 = $30

PV of coupon = discount factor*coupon

Price of bond = sum of PV of coupons = $810.23

weight = PV of coupon/Price of bond

Duration = time in year of bond paid*weight

duration of bond = sum of duration of all coupon = 2.78 years

Year	discount factor	coupon	PV of coupon	Weight	duration
0.5	0.9608	$       30.00	$             28.82	0.03	0.02
1	0.9231	$       30.00	$             27.69	0.03	0.03
1.5	0.8869	$       30.00	$             26.61	0.03	0.04
2	0.8521	$       30.00	$             25.56	0.03	0.05
2.5	0.8187	$       30.00	$             24.56	0.03	0.07
3	0.7866	$ 1,030.00	$           810.23	0.86	2.58
		Price	$           943.48	Duration	2.78