What is the Macaulay duration of a bond with a coupon of 5.0 percent, seven years to maturity, and a current price of $1,050.70

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

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