In: Finance
Find the duration of the following bonds with yield to maturity of 6%
- 6% copon rate with payment frequency 2, 20 years of maturity:
- 9% coupon rate with frequency 2, 5 years of maturity
- 9% coupon rate with frequency 2, 20 year
| Year | First Bond | PV | PV*Year | 
| 0.5 | 30 | 29.55988 | 14.77994 | 
| 1 | 30 | 29.12621 | 29.12621 | 
| 1.5 | 30 | 28.69891 | 43.04837 | 
| 2 | 30 | 28.27788 | 56.55575 | 
| 2.5 | 30 | 27.86302 | 69.65755 | 
| 3 | 30 | 27.45425 | 82.36275 | 
| 3.5 | 30 | 27.05148 | 94.68017 | 
| 4 | 30 | 26.65461 | 106.6184 | 
| 4.5 | 30 | 26.26357 | 118.1861 | 
| 5 | 30 | 25.87826 | 129.3913 | 
| 5.5 | 30 | 25.49861 | 140.2424 | 
| 6 | 30 | 25.12453 | 150.7472 | 
| 6.5 | 30 | 24.75593 | 160.9136 | 
| 7 | 30 | 24.39275 | 170.7492 | 
| 7.5 | 30 | 24.03489 | 180.2616 | 
| 8 | 30 | 23.68228 | 189.4582 | 
| 8.5 | 30 | 23.33484 | 198.3461 | 
| 9 | 30 | 22.9925 | 206.9325 | 
| 9.5 | 30 | 22.65519 | 215.2243 | 
| 10 | 30 | 22.32282 | 223.2282 | 
| 10.5 | 30 | 21.99533 | 230.9509 | 
| 11 | 30 | 21.67264 | 238.399 | 
| 11.5 | 30 | 21.35469 | 245.5789 | 
| 12 | 30 | 21.0414 | 252.4968 | 
| 12.5 | 30 | 20.7327 | 259.1588 | 
| 13 | 30 | 20.42854 | 265.571 | 
| 13.5 | 30 | 20.12884 | 271.7393 | 
| 14 | 30 | 19.83353 | 277.6695 | 
| 14.5 | 30 | 19.54256 | 283.3671 | 
| 15 | 30 | 19.25586 | 288.8379 | 
| 15.5 | 30 | 18.97336 | 294.0871 | 
| 16 | 30 | 18.69501 | 299.1201 | 
| 16.5 | 30 | 18.42074 | 303.9422 | 
| 17 | 30 | 18.15049 | 308.5584 | 
| 17.5 | 30 | 17.88421 | 312.9737 | 
| 18 | 30 | 17.62184 | 317.1931 | 
| 18.5 | 30 | 17.36331 | 321.2213 | 
| 19 | 30 | 17.10858 | 325.063 | 
| 19.5 | 30 | 16.85759 | 328.7229 | 
| 20 | 1030 | 570.286 | 11405.72 | 
Duration = sum(PV*Year)/Sum(pv) =
| Duration | 
| 13.35945 | 
| Second Bond | PV | PV*Year | 
| 45 | 44.33981752 | 22.16990876 | 
| 45 | 43.68932039 | 43.68932039 | 
| 45 | 43.04836652 | 64.57254978 | 
| 45 | 42.41681591 | 84.83363182 | 
| 45 | 41.7945306 | 104.4863265 | 
| 45 | 41.18137467 | 123.544124 | 
| 45 | 40.57721418 | 142.0202496 | 
| 45 | 39.98191716 | 159.9276686 | 
| 45 | 39.39535357 | 177.2790911 | 
| 1045 | 901.4261797 | 4507.130898 | 
| Duration | 
| 4.24905113 | 
| Third Bond | PV | PV*Year | 
| 45 | 44.33982 | 22.16991 | 
| 45 | 43.68932 | 43.68932 | 
| 45 | 43.04837 | 64.57255 | 
| 45 | 42.41682 | 84.83363 | 
| 45 | 41.79453 | 104.4863 | 
| 45 | 41.18137 | 123.5441 | 
| 45 | 40.57721 | 142.0202 | 
| 45 | 39.98192 | 159.9277 | 
| 45 | 39.39535 | 177.2791 | 
| 45 | 38.8174 | 194.087 | 
| 45 | 38.24792 | 210.3635 | 
| 45 | 37.68679 | 226.1207 | 
| 45 | 37.1339 | 241.3703 | 
| 45 | 36.58912 | 256.1238 | 
| 45 | 36.05233 | 270.3925 | 
| 45 | 35.52342 | 284.1873 | 
| 45 | 35.00226 | 297.5192 | 
| 45 | 34.48875 | 310.3988 | 
| 45 | 33.98278 | 322.8364 | 
| 45 | 33.48423 | 334.8423 | 
| 45 | 32.99299 | 346.4264 | 
| 45 | 32.50896 | 357.5985 | 
| 45 | 32.03203 | 368.3683 | 
| 45 | 31.56209 | 378.7451 | 
| 45 | 31.09906 | 388.7382 | 
| 45 | 30.64281 | 398.3565 | 
| 45 | 30.19326 | 407.609 | 
| 45 | 29.7503 | 416.5042 | 
| 45 | 29.31384 | 425.0507 | 
| 45 | 28.88379 | 433.2568 | 
| 45 | 28.46004 | 441.1306 | 
| 45 | 28.04251 | 448.6802 | 
| 45 | 27.63111 | 455.9133 | 
| 45 | 27.22574 | 462.8376 | 
| 45 | 26.82632 | 469.4606 | 
| 45 | 26.43276 | 475.7896 | 
| 45 | 26.04497 | 481.8319 | 
| 45 | 25.66287 | 487.5946 | 
| 45 | 25.28638 | 493.0844 | 
| 1045 | 578.5912 | 11571.82 | 
| Duration | 
| 12.39323 |