Question

What is the Macaulay duration of a bond with a coupon of 6.6 percent, seven years to maturity, and a current price of $1,069.40? What is the modified duration? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Answer 1

K = N

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

k=1

K =7

1069.4 =∑ [(6.6*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^7

k=1

YTM% = 5.38

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($1,069.40)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	66.00	1.05	62.63	62.63
2	66.00	1.11	59.43	118.87
3	66.00	1.17	56.40	169.20
4	66.00	1.23	53.52	214.08
5	66.00	1.30	50.79	253.94
6	66.00	1.37	48.19	289.17
7	1,066.00	1.44	738.67	5,170.68
			Total	6,278.55

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

=6278.55/(1069.4*1)

=5.871

Modified duration = Macaulay duration/(1+YTM)

=5.87/(1+0.0538)

=5.571