Question

I just remember some keywords for a question: Semiannually, coupon rate =11%, 3 years to maturity, yield to maturity =10%, face value at 1000

How to solve for the duration for this question?

Answer 1

K = Nx2

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

k=1

K =3x2

Bond Price =∑ [(11*1000/200)/(1 + 10/200)^k]     +   1000/(1 + 10/200)^3x2

k=1

Bond Price = 1025.38

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,025.38)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	55.00	1.05	52.38	52.38
2	55.00	1.10	49.89	99.77
3	55.00	1.16	47.51	142.53
4	55.00	1.22	45.25	180.99
5	55.00	1.28	43.09	215.47
6	1,055.00	1.34	787.26	4,723.54
			Total	5,414.70

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

=5414.7/(1025.38*2)

=2.640336