Question

Calculate the duration of a 2 year bond that pays semiannually and has a 7% yield if the coupon rate is 6%.

1.81

1.86

1.91

1.96

None of the above

Answer 1

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =2x2

Bond Price =∑ [(6*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^2x2

k=1

Bond Price = 981.63

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($981.63)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.04	28.99	28.99
2	30.00	1.07	28.01	56.01
3	30.00	1.11	27.06	81.17
4	1,030.00	1.15	897.59	3,590.34
			Total	3,756.51

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

=3756.51/(981.63*2)

=1.91