Question

A 20 year bond has annual coupons of 400. The bond matures for 13,000.

Calculate the Macaulay Duration of this bond at an annual effective rate of 5.1%.

Answer 1

Given

M=13000

n=20

y=5.1%

C=400

Bond Price P=C*(1-(1+y)^-n)/y + M/(1+y)^n

P=400*(1-(1+5.1%)^-20)/5.1% + 13000/(1+5.1%)^20 =$9750.05

Macaulay duration = MD

MD=14.36 Years

t	t*400/(1+5.1%)^t
1	380.59
2	724.24
3	1033.65
4	1311.32
5	1559.61
6	1780.72
7	1976.69
8	2149.45
9	2300.80
10	2432.39
11	2545.79
12	2642.46
13	2723.75
14	2790.94
15	2845.18
16	2887.60
17	2919.19
18	2940.92
19	2953.67
20	2958.26
∑t*400/(1+5.1%)^t	43857.23