Given face value = 100, coupon bond of 5%, period = 3 years.
Case 1) when ytm = 6%
Bond duration =
Period | coupon | pv factor for ytm 6% | pv of coupon | pv/ price | (pv/price)*period |
-0.5 | 25 | 0.9708 | 24.27 | 0.1107 | 0.055 |
-1 | 25 | 0.9426 | 23.56 | 0.1075 | 0.1075 |
-1.5 | 25 | 0.9151 | 22.88 | 0.1044 | 0.1566 |
-2 | 25 | 0.8884 | 22.21 | 0.1013 | 0.2026 |
-2.5 | 25 | 0.8625 | 21.56 | 0.0983 | 0.2457 |
-3 | 25+100(fv) | 0.8374 | 104.675 | 0.4776 | 1.433 |
219.15 | 2.20 |
Hence bond duration = 2.2 years.
Case 2)
Similarly bond duration for ytm = 8% is 2.184 years. Detailed calculations in the attached.
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