Using the ULTIMATE mortality rates in Appendix Dandi = 10%, and the following random variable: 0.1 Appendix D Ultimate X PX P(death) , RV RV PV of annuity of $1,000 per year payable annually, starting today, while a life now aged 30 stays alive Note: P, values from Appendix D are shown here in colunns N-O, for convenience Find: expected value variance Your client plans to sell 100 of these annuities to lives aged 30 (enough for the Central Limit Theorem to apply). Find the 95% confidence interval for the AVERAGE present value of the 100 annuities: low end high end 20 0.999750361 21 0.999746683 22 0.999742549 23 0.999737902 24 0.999732679 25 0.999726808 26 0.999720209 27 0.999712792 28 0.999704456 29 0.999695086 30 0.999684554 31 0.999672716 32 0.999659411 33 0.999644456 34 0.999627647 35 0.999608754 36 0.999587518 37 0.99956365 38 0.999536823 39 0.99950667 40 0.99947278 41 0.999434688 42 0.999391874 43 0.999343754 44 0.99928967 45 0.999228883 46 0.999160563 47 0.999083776 48 0.998997475 49 0.998900482 50 0.998791473 0.000315 10868.97 1 1 0.000327 10859.3 1.909090909 3.644628 0.00034 10848.78 2.73553719 7.483164 0.000355 10837.35 3.486851991 12.15814 0.000372 10824.93 4.169865446 17.38778 0.000391 10811.45 4.790786769 22.95164 0.000412 10796.82 5.355260699 28.67882 0.000435 10780.95 5.868418818 34.43834 0.000462 10763.74 6.334926198 40.13129 0.000492 10745.09 6.759023816 45.6844 0.000525 10724.89 7.144567106 51.04484 0.000563 10703.02 7.495061005 56.17594 0.000605 10679.36 7.813691823 61.05378 0.000653 10653.78 8.103356203 65.66438 0.000706 10626.13 8.366687457 70.00146 0.000766 10596.27 8.606079506 74.0646 0.000833 10564.04 8.823708642 77.85783 0.000908 10529.28 9.021553311 81.38842 0.000993 10491.82 9.201412101 84.66598 0.001088 10451.48 9.364920092 87.70173 0.001195 10408.07 9.51356372 90.50789 Using the ULTIMATE mortality rates in Appendix Dandi = 10%, and the following random variable: 0.1 Appendix D Ultimate X PX P(death) , RV RV PV of annuity of $1,000 per year payable annually, starting today, while a life now aged 30 stays alive Note: P, values from Appendix D are shown here in colunns N-O, for convenience Find: expected value variance Your client plans to sell 100 of these annuities to lives aged 30 (enough for the Central Limit Theorem to apply). Find the 95% confidence interval for the AVERAGE present value of the 100 annuities: low end high end 20 0.999750361 21 0.999746683 22 0.999742549 23 0.999737902 24 0.999732679 25 0.999726808 26 0.999720209 27 0.999712792 28 0.999704456 29 0.999695086 30 0.999684554 31 0.999672716 32 0.999659411 33 0.999644456 34 0.999627647 35 0.999608754 36 0.999587518 37 0.99956365 38 0.999536823 39 0.99950667 40 0.99947278 41 0.999434688 42 0.999391874 43 0.999343754 44 0.99928967 45 0.999228883 46 0.999160563 47 0.999083776 48 0.998997475 49 0.998900482 50 0.998791473 0.000315 10868.97 1 1 0.000327 10859.3 1.909090909 3.644628 0.00034 10848.78 2.73553719 7.483164 0.000355 10837.35 3.486851991 12.15814 0.000372 10824.93 4.169865446 17.38778 0.000391 10811.45 4.790786769 22.95164 0.000412 10796.82 5.355260699 28.67882 0.000435 10780.95 5.868418818 34.43834 0.000462 10763.74 6.334926198 40.13129 0.000492 10745.09 6.759023816 45.6844 0.000525 10724.89 7.144567106 51.04484 0.000563 10703.02 7.495061005 56.17594 0.000605 10679.36 7.813691823 61.05378 0.000653 10653.78 8.103356203 65.66438 0.000706 10626.13 8.366687457 70.00146 0.000766 10596.27 8.606079506 74.0646 0.000833 10564.04 8.823708642 77.85783 0.000908 10529.28 9.021553311 81.38842 0.000993 10491.82 9.201412101 84.66598 0.001088 10451.48 9.364920092 87.70173 0.001195 10408.07 9.51356372 90.50789
