Question

Find the duration of a 6.0% coupon bond making annual coupon payments if it has four years to maturity and a yield to maturity of 5.0%. (assuming a face value of $1,000)

	A.	4.54 Years
	B.	4.00 Years
	C.	3.82 Years
	D.	5.00 Years
	E.	3.68 Years
	F.	4.48 Years

Answer 1

Face Value of the bond = $1000

Annual coupon rate = 6%

Annual coupon payment = Annual coupon rate*Face Value = 6%*1000 = 60

YTM = 5%

The cashflow for the bond is:

C₁ = 60, C₂ = 60, C₃ = 60, C₄ = 1060

Year	Cashflow
1	60
2	60
3	60
4	1,060

Present value of C₁ = PV₁ = C₁/(1+YTM)¹ = 60/(1+5%)¹ = 57.1428571428571

Present value of C₂ = PV₂ = C₂/(1+YTM)² = 60/(1+5%)² = 54.421768707483

Present value of C₃ = PV₃ = C₃/(1+YTM)³ = 60/(1+5%)³ = 51.8302559118886

Present value of C₄ = PV₄ = C₄/(1+YTM)⁴ = 1060/(1+5%)⁴ = 872.064623279395

We know that price of the bond is the sum of the present value of all the cash flows

Price of the Bond = P = PV₁ + PV₂ + PV₃ + PV₄ = 57.1428571428571 + 54.421768707483 + 51.8302559118886 + 872.064623279395 = 1035.45950504162

Now, Duration is calculated using the formula:

Duration = [(1*57.1428571428571)+(2*54.421768707483)+(3*51.8302559118886)+(4*872.064623279395)]/1035.45950504162 = 3809.73565541107/1035.45950504162 = 3.67927054304062 ~ 3.68 years(Rounded to two decimals)

Answer -> 3.68 years (Option E)