Question

What is the Macaulay duration of a semiannual-pay 7.62 percent coupon bond with 11 years to maturity and a yield to maturity of 6.06 percent?

The correct answer is 7.851. How do you get that? Using the Macaulay duration formula, not excel.

Answer 1

K = Nx2

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

k=1

K =11x2

Bond Price =∑ [(7.62*1000/200)/(1 + 6.06/200)^k]     +   1000/(1 + 6.06/200)^11x2

k=1

Bond Price = 1123.94

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($1,123.94)
1	38.10	36.98	36.98
2	38.10	35.89	71.78
3	38.10	34.84	104.51
4	38.10	33.81	135.25
5	38.10	32.82	164.09
6	38.10	31.85	191.11
7	38.10	30.92	216.41
8	38.10	30.01	240.05
9	38.10	29.12	262.12
10	38.10	28.27	282.68
11	38.10	27.44	301.80
12	38.10	26.63	319.55
13	38.10	25.85	336.00
14	38.10	25.09	351.21
15	38.10	24.35	365.23
16	38.10	23.63	378.12
17	38.10	22.94	389.93
18	38.10	22.26	400.73
19	38.10	21.61	410.55
20	38.10	20.97	419.45
21	38.10	20.36	427.47
22	1,038.10	538.32	11,842.97
		Total	17,647.98

where PV of cash flow = cashflow/(1+YTM/2)^corresponding period

duration calc = PV of cash flow*corresponding period

numerator = sum of all duration calc = 17647.98

denominator = bond price

macaulay duration = 17647.98/1123.94/2=7.85

note above formula there is a divide by 2 because frequency of payment is semi annual