Question

A bond has payments of $100 in one year, $100 the following year, and then $1,100 the year after that. If the discount rate is 6%, what is the Macaulay Duration of this set of payments?

Answer 1

K = N

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

k=1

K =3

Bond Price =∑ [(10*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^3

k=1

Bond Price = 1106.92

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,106.92)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	100.00	1.06	94.34	94.34
2	100.00	1.12	89.00	178.00
3	1,100.00	1.19	923.58	2,770.74
			Total	3,043.08

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

=3043.08/(1106.92*1)

=2.749144