Question

Calculate the duration of a 2 year bond that pays semiannually and has a 7% yield if the coupon rate goes up to 8%.

1.86

1.89

1.92

1.95

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 =∑ [(8*1000/200)/(1 + 7/200)^k]     +   1000/(1 + 7/200)^2x2

k=1

Bond Price = 1018.37

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,018.37)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	40.00	1.04	38.65	38.65
2	40.00	1.07	37.34	74.68
3	40.00	1.11	36.08	108.23
4	1,040.00	1.15	906.30	3,625.20
			Total	3,846.76

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

=3846.76/(1018.37*2)

=1.89