Question

A T-bond with semi-annual coupons has a coupon rate of 3%, 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

Answer 1

K = Nx2

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

k=1

K =2x2

Bond Price =∑ [(3*1000/200)/(1 + 4/200)^k]     +   1000/(1 + 4/200)^2x2

k=1

Bond Price = 980.96

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($980.96)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	15.00	1.02	14.71	14.71
2	15.00	1.04	14.42	28.84
3	15.00	1.06	14.13	42.40
4	1,015.00	1.08	937.70	3,750.81
			Total	3,836.76

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

=3836.76/(980.96*2)

=1.956