In: Finance
What is the bond’s Macaulay duration of a 2.5 years, 8 percent semiannual coupon bond selling at par of $1,000?
A. 2.5 years. |
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B. 2.45 years. |
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C. 1.94 years. |
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D. 2.31 years. |
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E. 1.75 years |
Period (in years) |
Payment | Present value factor | Present value | Duration |
0.50 | $ 40.00 | 0.961538462 | $ 38.46 | $ 19.23 |
1.00 | $ 40.00 | 0.924556213 | $ 36.98 | $ 36.98 |
1.50 | $ 40.00 | 0.888996359 | $ 35.56 | $ 53.34 |
2.00 | $ 40.00 | 0.854804191 | $ 34.19 | $ 68.38 |
2.50 | $ 1,040.00 | 0.821927107 | $ 854.80 | $ 2,137.01 |
$ 1,000.00 | $ 2,314.95 | |||
Macaulay duration | 2.31 |
Macaulay duration = $2,314.95 / $1,000 = 2.31 years
Answer is 2.31 years
Each period interest = $1,000 X 8% X 6/12 = $40
Last period payment = $40 + $1,000 principal = $1,040
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