Question

A T-bond with semi-annual coupons has a coupon rate of 7%, face value of $1,000, and 2 years to maturity. If its yield to maturity is 5%, 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 =∑ [(7*1000/200)/(1 + 5/200)^k]     +   1000/(1 + 5/200)^2x2

k=1

Bond Price = 1037.62

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,037.62)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	35.00	1.03	34.15	34.15
2	35.00	1.05	33.31	66.63
3	35.00	1.08	32.50	97.50
4	1,035.00	1.10	937.66	3,750.64
			Total	3,948.91

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

=3948.91/(1037.62*2)

=1.903