Question

Bond A has a 9% coupon rate, paid annually. Maturity is in three years. The bond sells at par value $1000.  The modified duration of this bond is ___and the dollar duration of this bond is ___.

	A.	2.78, 2780
	B.	2.81, 2810
	C.	2.76, 2760
	D.	2.65, 2650

Answer 1

Given for the bond,

Face value = $1000

Coupon rate = 9% annually

annual coupon = 9%*1000 = $90

bond is selling at par

So, YTM = coupon rate = 9%

Duration is calculated as below table:

PV of coupon = coupon/(1+YTM)^year

Price = sum of all PV = $1000

weight = PV of coupon/ price

duration of each coupon = year*weight

duration of the bond = sum of all duration = 2.76 years

Year	coupon	PV of coupon=coupon/(1+YTM)^year	weight = PV of Coupon/Price	Duration = weight*year
1	$                90.00	$                82.57	0.0826	0.0826
2	$                90.00	$                75.75	0.0758	0.1515
3	$          1,090.00	$             841.68	0.8417	2.5250
	Price	$          1,000.00	Duration	2.76

So, duration of the bond is 2.76

Dollar duration = duration*price = 2.76*1000 = $2760

OptionC is correct.