Question

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Find the duration of the following bonds with yield to maturity of 6% - 6% copon...

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

Solutions

Expert Solution

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

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