Question

A T-bond with semi-annual coupons has a coupon rate of 6%, face value of $1,000, and 2 years to maturity. If its yield to maturity is 4%, what is its Macaulay Duration? Answer in years, rounded to three decimal places. Please show your work. Thank you.

Answer 1

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(6*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^2x2

k=1

Bond Price = 1038.08

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,038.08)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	30.00	1.02	29.41	29.41
2	30.00	1.04	28.84	57.67
3	30.00	1.06	28.27	84.81
4	1,030.00	1.08	951.56	3,806.24
			Total	3,978.13

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

=3978.13/(1038.08*2)

=1.916