Question

Consider the following. a. What is the duration of a four-year Treasury bond with a 8 percent semiannual coupon selling at par?

b. What is the duration of a three-year Treasury bond with a 8 percent semiannual coupon selling at par?

c. What is the duration of a two-year Treasury bond with a 8 percent semiannual coupon selling at par? (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

A 3.5years

B ? years

C ?years

Answer 1

	Present Value (PV) of Cash Flow:
	(Cash Flow)/((1+i)^N)
	i=Discount Rate=Interest rate
	N=Year of Cash Flow
	a	Four-year Treasury bond with a 8 percent semiannual coupon selling at par
	Semiannual interest rate=(8/2)%=4%=	0.04
	Discount Rate=0.04
	Assuming Face value=$1000
		N	A	B=N*A	C=B/(1.04^N)
		Semi-annual Period	Cash Flow	Period * Cashflow	Present value of (Period* Cashflow)
		1	40	40	38.46153846
		2	40	80	73.96449704
		3	40	120	106.679563
		4	40	160	136.7686706
		5	40	200	164.3854214
		6	40	240	189.6754862
		7	40	280	212.7769877
		8	1040	8320	6079.342506
				SUM	7002.05
	Bond Duration	7.002	Semiannualperiod		(7002.05/1000)
	Bond Duration in Years	3.5	Years	(7.002/2)
	a	Three-year Treasury bond with a 8 percent semiannual coupon selling at par
	Semiannual interest rate=(8/2)%=4%=	0.04
	Discount Rate=0.04
	Assuming Face value=$1000
		N	A	B=N*A	C=B/(1.04^N)
		Semi-annual Period	Cash Flow	Period * Cashflow	Present value of (Period* Cashflow)
		1	40	40	38.46153846
		2	40	80	73.96449704
		3	40	120	106.679563
		4	40	160	136.7686706
		5	40	200	164.3854214
		6	1040	6240	4931.562641
				SUM	5451.82
	Bond Duration	5.452	Semiannualperiod		(5451.82/1000)
	Bond Duration in YEARS	2.7	Years	(5.452/2)
	a	Two-year Treasury bond with a 8 percent semiannual coupon selling at par
	Semiannual interest rate=(8/2)%=4%=	0.04
	Discount Rate=0.04
	Assuming Face value=$1000
		N	A	B=N*A	C=B/(1.04^N)
		Semi-annual Period	Cash Flow	Period * Cashflow	Present value of (Period* Cashflow)
		1	40	40	38.46153846
		2	40	80	73.96449704
		3	40	120	106.679563
		4	1040	4160	3555.985435
				SUM	3775.09
	Bond Duration	3.775	Semiannualperiod		(3775.09/1000)
	Bond Duration	1.9	Years	(3.775/2)
	ANSWER:
	A	3.5	Years
	B	2.7	Years
	C	1.9	Years