We need to find the macaulay duration , which is the weighted sum of the present values of the cash flows as shown in the table below,
year(Tf) | Cash flow | PV of Cash Flow @YTM =6% [ CF / (1+ YTM)^f] | (PV/Total)(Tf) | PV of Cah Flow @YTM =10% [ CF / (1+ YTM)^f] | (PV/Total)(Tf) |
0.5 | 3.6 | 3.495145631 | 0.016925593 | 3.428571429 | 0.018454207 |
1 | 3.6 | 3.393345273 | 0.032865229 | 3.265306122 | 0.035150871 |
1.5 | 3.6 | 3.294509974 | 0.047861984 | 3.109815355 | 0.05021553 |
2 | 3.6 | 3.198553372 | 0.061957261 | 2.961728909 | 0.063765753 |
2.5 | 3.6 | 3.105391624 | 0.075190851 | 2.820694199 | 0.07591161 |
3 | 103.6 | 86.76336899 | 2.520961871 | 77.30791509 | 2.49664852 |
Total | 103.2503149 | 2.755762791 | 92.89403111 | 2.740146492 |
The duration for YTM @6% is 2.755 yrs
The duration for YTM @10% is 2.740 yrs
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