Question

a. Calculate the duration of a 6 percent, $1,000 par bond maturing in three years if the yield to maturity is 10 percent and interest is paid semiannually. b. Calculate the modified duration for a 10-year, 12 percent bond with a yield to maturity of 10 percent and a Macaulay duration of 7.2 years.

Answer 1

a.

K = Nx2

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

k=1

K =3x2

Bond Price =∑ [(6*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^3x2

k=1

Bond Price = 898.49

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($898.49)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.05	28.57	28.57
2	30.00	1.10	27.21	54.42
3	30.00	1.16	25.92	77.75
4	30.00	1.22	24.68	98.72
5	30.00	1.28	23.51	117.53
6	1,030.00	1.34	768.60	4,611.61
			Total	4,988.60

As it is not mentioned which duration, I have calculated both as following

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

=4988.6/(898.49*2)

=2.78

Modified duration = Macaulay duration/(1+YTM)

=2.78/(1+0.1)

=2.64

b.

modified duration = macaulay duration/(1+YTM) = 7.2/(1+0.1) = 6.5454%