Answer:
5.78 years
Explanation:
face value = $1,000
market price = $1,050.70
assuming that the bond pays an annual coupon:
period 1 cash flow = $50
period 2 cash flow = $50
period 3 cash flow = $50
period 4 cash flow = $50
period 5 cash flow = $50
period 6 cash flow = $50
period 7 cash flow = $1,050
period 1 discount factor = 1/1.05 = 0.952
period 2 discount factor = 1/1.05² = 0.907
period 3 discount factor = 1/1.05³ = 0.864
period 4 discount factor = 1/1.05⁴ = 0.823
period 5 discount factor = 1/1.05⁵ = 0.784
period 6 discount factor = 1/1.05⁶ = 0.746
period 7 discount factor = 1/1.05⁷ = 0.711
now we multiply:
period 1 = 1 x $50 x 0.952 = $47.60
period 2 = 2 x $50 x 0.907 = $90.70
period 3 = 3 x $50 x 0.864 = $129.60
period 4 = 4 x $50 x 0.823 = $164.60
period 5 = 5 x $50 x 0.784 = $196
period 6 = 6 x $50 x 0.746 = $223.80
period 7 = 7 x $1,050 x 0.711 = $5,225.85
total = $6,078.15
Macauly duration = $6,078.15 / $1,050.70 = 5.78 years
