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 |