Question

An investment has the following payoffs: $50 in one year, $50 in two years, $50 in three years, and $1,050 in four years. The investment has a YTM of 4%. Calculate the duration (Macaulay duration, not modified duration).

Give your answer to two decimal places.

Answer 1

Year (x)	Cash flow	Present value (w)	wx
1	50	50 / 1.04 = 48.08	48.08
2	50	50 / 1.042 = 46.2278	92.4556
3	50	50 / 1.043 = 44.45	133.35
4	1050	1050 / 1.044 = 897.54	3590.16
		1036.3022	4761.59

Macauley Duration = Sum of Wx / Sum of W

                           = 4761.59 / 1036.3022

                           = 4.60 years Answer