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Calculate the Macaulay duration, Macaulay convexity, and dispersion of a 10-year bond with semiannual coupons paid at 6% per year earning an annual effective yield

Calculate the Macaulay duration, Macaulay convexity, and dispersion of a 10-year bond with semiannual coupons paid at 6% per year earning an annual effective yield of 11%

Answer:

T(Term) DF @ 11% /2=5.5% Cash Flow 1000*6% semi annually PV Duration PV*T*(T+1)
0.5 0.947867 60.00 56.87 28.44 42.65402844
1 0.898452 60.00 53.91 53.91 107.8142899
1.5 0.851614 60.00 51.10 76.65 191.6130744
2 0.807217 60.00 48.43 96.87 290.5980276
2.5 0.765134 60.00 45.91 114.77 401.6955358
3 0.725246 60.00 43.51 130.54 522.1769998
3.5 0.687437 60.00 41.25 144.36 649.6277841
4 0.651599 60.00 39.10 156.38 781.9186448
4.5 0.617629 60.00 37.06 166.76 917.179453
5 0.585431 60.00 35.13 175.63 1053.775043
5.5 0.554911 60.00 33.29 183.12 1190.283026
6 0.525982 60.00 31.56 189.35 1325.473426
6.5 0.498561 60.00 29.91 194.44 1458.289992
7 0.472569 60.00 28.35 198.48 1587.833069
7.5 0.447933 60.00 26.88 201.57 1713.343909
8 0.424581 60.00 25.47 203.80 1834.190301
8.5 0.402447 60.00 24.15 205.25 1949.853434
9 0.381466 60.00 22.89 205.99 2059.915884
9.5 0.361579 60.00 21.69 206.10 2164.050652
10 0.342729 1,060.00 363.29 3,632.93 39962.19712
1,059.75 6,565.33 60,204.48
Duration of the bond 6565.33/1059.75 6.20
Convexity 60204.483697857/1060

56.80

QUESTION: What are the exact calculations to how these answers are formed?

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