Question

You intend to purchase a 1-year, $1,000 face value bond. Coupon rate of this bond is 8%. Market interest rate is 5 percent. Coupon payments are semiannual, what is the duration of the bond? (Answer is rounded)

Answer 1

Given for the bond,

Face value = $1000

Coupon rate = 8% semiannually

coupon = (8%/2)*100 = $40

Yield to maturity = 5% compounded semiannually

Duration is calculated as below table:

here, since it is a semiannual bond, discount factor = 1/(1+YTM/2)^(2*period)

PV of coupon = discount factor * coupon

Price = sum of all PV = $1028.91

weight = PV of coupon/ price

duration of each coupon = year*weight

duration of the bond = sum of all duration = 0.98 years

In term of semiannual period, duration = 2*0.98 = 1.96 periods

Year	Period	Coupon	Discount factor = 1/(1+YTM/3)^(3*year)	PV of cash flow=coupon*discount factor	weight = PV of Coupon/Price	Duration = weight*year
0.5000	1	$                40.00	$                  0.98	$                39.02	0.0379	0.0190
1.0000	2	$          1,040.00	$                  0.95	$             989.89	0.9621	0.9621
			Price	$          1,028.91	Duration	0.9810