Question

A bond pays annual interest. Its coupon rate is 11.0%. Its value at maturity is $1000. It matures in 4 years. Its yield to maturity is currently 8.00%. The modified duration of this bond is ________ years. 3.47 2.97 4.00 3.21

Answer 1

K = N

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

k=1

K =4

Bond Price =∑ [(11*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^4

k=1

Bond Price = 1099.36

Duration

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,099.36)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	110.00	1.08	101.85	101.85
2	110.00	1.17	94.31	188.61
3	110.00	1.26	87.32	261.96
4	1,110.00	1.36	815.88	3,263.53
			Total	3,815.96

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

=3815.96/(1099.36*1)

=3.471077

Modified duration = Macaulay duration/(1+YTM)

=3.47/(1+0.08)

=3.21396