Question

Assume a bond has a 1000 par value and a 5 percent coupon rate, two year remaining to maturity, and a 10 percent yield to maturity. What is the duration of this bond?

A. 2

B. 1.97

C. 1.95

D. 1.83

Answer is C. I need to know how, please show work!

Answer 1

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =2

Bond Price =∑ [(5*1000/100)/(1 + 10/100)^k]     +   1000/(1 + 10/100)^2

k=1

Bond Price = 913.22

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($913.22)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	50.00	1.10	45.45	45.45
2	1,050.00	1.21	867.77	1,735.54
			Total	1,780.99

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=1780.99/(913.22*1)

=1.950