人寿保险费额的计算（实验6）
报告人：陈示旦（05123120）葛凯明（05123126）张玲玲（05123114）实验问题
根据生命表计算单位保费终身寿险的趸缴保费，A x以及2A x。
问题分析
根据计算公式，当t→∞时，A x=Σv k+1*k|q x= Σv k+1*k p x q x+k （1）
q x=d x+k/l x，可从生命表直接获得，（1）两边同乘l x
k|
l x A x= A x=Σv k+1*d x+k, 由v k+1*k p x q x+k= v k+1* d x+k/l x= v x+k+1/ v x l x
计算过程
设D x=v^x*l，C x=v^(v+1)*d x，M x=Σ(C x+k)，
则A x= Σv k+1*k p x q x+k=ΣC x+k/D x= M x/D x
将生命表中数据以及v=1/(1+i)=1/1.06代入以上等式，可得A x
将生命表中数据以及v2=1/(1+i) 2=1/1.062代替v代入以上等式，可得2A x
实验结果
利用Excel，得出以下结果
v=1/1.06= 0.943396226 v^2=1/1.06^2= 0.8899964
年龄
l x
（生存人数）
d x
（死亡人数）1000q x D x=v^x*l C x=v^(v+1)*d x M x=sum(C x+k) A x D x=v^x*l C x=v^(v+1)*d x M x=sum(C x+k) 2A x
0 100000 2042.17 20.4217 100000 1926.57547 5152.947937 0.05153 100000 1817.52403 2603.619887 0.02604
1 97957.83 131.567
2 1.3431 92413.047 117.09434 3226.372465 0.03491 87182.12 104.2135454 786.0958571 0.00902
2 97826.26 119.71 1.2237 87065.02
3 100.51082
4 3109.27812
5 0.03571 77487.561 84.3908263 681.8823117 0.0088
3 97706.55 109.812
4 1.1239 82036.303 86.9817062 3008.767301 0.03668 68879.262 68.89765829 597.4914854 0.00867
4 97569.74 101.7056 1.0421 77284.373 76.0003408 2921.78559
5 0.03781 61216.462 56.79187582 528.5938272 0.00863
5 97459.03 95.252
6 0.97
7 72827.057 67.1493244 2845.785254 0.0390
8 54420.613 47.337624 471.8019513 0.00867
6 97399.78 90.2799 0.9269 68663.002 60.041289
7 2778.63593 0.04047 48404.707 39.93088683 424.4643273 0.00877
7 97309.5 86.6444 0.8904 64716.375 54.3617685 2718.59464 0.04201 43040.086 34.10724606 384.5334405 0.00893
8 97222.86 84.195 0.866 60998.825 49.8348911 2664.232871 0.04368 38271.418 29.49719549 350.4261944 0.00916
9 97138.66 82.7816 0.8522 57496.224 46.2248131 2614.39798 0.04547 34031.926 25.81169418 320.9289989 0.00943
10 97055.88 82.2549 0.8475 54195.496 43.3308552 2568.173167 0.04739 30262.482 22.826154 295.1173048 0.00975
11 96973.63 82.4664 0.8504 51084.499 40.9832743 2524.842312 0.04942 26910.677 20.36743176 272.2911508 0.01012
12 96891.16 83.2842 0.8596 48151.938 39.0468829 2483.859038 0.05158 23930.038 18.3067024 251.923719 0.01053
13 96807.88 84.518 0.873 45387.312 37.3823929 2444.812155 0.05387 21279.343 16.53426843 233.6170166 0.01098
14 96723.36 86.0611 0.8898 42780.835 35.9102901 2407.429762 0.05627 18922.005 14.98410939 217.0827482 0.01147
15 96637.3 87.7559 0.9081 40323.369 34.5447839 2371.519472 0.05881 16825.533 13.59842581 202.0986388 0.01201
16 96549.54 89.6167 0.9282 38006.368 33.2804537 2336.974688 0.06149 14961.065 12.35917634 188.500213 0.0126
17 96459.92 91.6592 0.9502 35821.782 32.1122316 2303.694234 0.06431 13302.935 11.25032097 176.1410366 0.01324
18 96368.26 93.9005 0.9744 33762.022 31.0353369 2271.582003 0.06728 11828.315 10.25758264 164.8907157 0.01394
19 96274.36 96.3596 1.0009 31819.929 30.0453788 2240.546666 0.07041 10516.9 9.368291119 154.633133 0.0147
20 96178 99.0569 1.0299 29988.755 29.138**** ****.501287 0.07371 9350.6356 8.571136103 145.2648419 0.01554
21 96078.95 102.0149 1.0618 28262.142 28.3096547 2181.363165 0.07718 8313.4618 7.856073474 136.6937058 0.01644
