1、五章节生存年金趸缴纯保费1nnxxx nnx nx nx nx nnxxxxxEllvvlvlNElv lN xNn现时支付法是将时刻t的年金给付额折现至签单时的现值，再将所有的现值相加或积分。n总额支付法是先求出在未来寿命期限内所有可能年金给付额的现值，再求现值的数学期望n两种方法是等价的n符号介绍：n精算折现因子n精算累积因子1nnxx:nxnE=A=vp nx1ExxxDNa xa xl、x+1x+2x+3lllxa2xxx+1x+22xx+1x+2xx+1x+2xx+1x+2xxxxl=l+vl+v l+l+vl+v l+Lv l+vl+vl+a=lv l xxxv l=Dx xx x
2、x x+1 1x x+2 2N N=D D+D D+D D+xxxa=NDxnxxn:xD)N(Na xxxDNa xnxx|nDNa xnmxmxxn|mD)N(Na k k+1N N xxxDS)a(I xxx+1x+2S=N+N+N+x1xxDS(Ia)x xx x+n nx x+n nx x:n nx xS S-S S-n nN N(I Ia a)=D D111x x+x x+n n+x x+n n+x x:n nx xS S-S S-n nN N(I Ia a)=D D元每年年金领取额8703x26606305710 xDNx 1000006060元趸缴纯保费148511485193
3、943939432668126681-30571030571050005000D DN NN N 50005000404080806060n|xnxx+nn|xnxx+na=E a=E a anna n|xn|xx:x:a=-aa=-anxnnE1x:x:x:x:a=aa=ax11vpxx+xx+a=+aa=+ann|xn|x nxn|xn|x nxa=a-Ea=a-Ennx1vpn|xx+n|xx+a=aa=an xxxDMAAxxlxdddd、x+1x+2x+33x1231212AddddddA2xxx+x+2x+x+xx+x+xx+1xxxxl=v+v l+v l+v+v+v+v+v+=
4、lv l 1dCx+xxv=MCCCx xx xx x+1 1x x+2 2=+xxxDMAxnxxn:x1D)M(MAxxxDMA xnxxnxxn:xDDD)M(MARAx xx xx x(I I)=D D1RRMAx xx x+n nx x+n nx x:n nx x-n n(I I)=D D111M(RR)DAx xx x+x x+n n+x x:n nx xn n-()=D D0.54390.54390.01830.01833 351091/939451091/9394434311729)/93911729)/939-(13451(134514040D D5050D D4040D D
5、)5050M M4040(M(M1元保额趸缴纯保费1元保额趸缴纯保费元万保额的趸缴纯保费5621554385183010不同死亡率的保费比较表不同死亡率的保费比较表（）n每千元终身寿险保额的趸缴纯保费（利率每千元终身寿险保额的趸缴纯保费（利率2.5%2.5%）362.92362.92368.01368.01372.90372.90377.60377.60382.12382.12371.54371.54376.74376.74381.73381.73386.53386.53391.15391.15380.38380.38385.70385.70390.79390.79395.69395.6940
6、0.40400.40389.44389.44394.87394.87400.07400.07405.07405.07409.89409.89398.72398.72404.26404.26409.58409.58414.69414.69419.60419.60408.22408.22413.88413.88419.31419.31424.53424.53429.55429.55417.93417.93423.72423.72429.27429.27434.60434.60439.73439.73427.87427.87433.79433.79439.46439.46444.90444.9045
7、0.15450.15438.04438.04444.08444.08449.88449.88455.44455.44460.80460.80448.44448.44454.61454.61460.53460.53466.22466.22471.69471.69459.07459.07465.37465.37471.42471.42477.23477.23482.83482.83不同利率的费率比较表（不同利率的费率比较表（）利率利率年龄年龄2.5%4%6%8%303732201187031382228124753239123613179334002451388534409254145903541
8、926315296364292731601023743928316910938450294177116394613041871234047131519613112(1+i)/ixx1daAx:nx:n1daA11m|x:nx:mx+m:nA=AAttx:txx+A=(vp)A11x:nx:hx:nx:hApaA pan n 10000013305)-(146061328074)-(2573730y100000DMMDNNy3141313141311 12032203232:2032:2032:2032:20PPa=20A+1/2a=20A+1/220P20P E E4040:2040:20pa10000A0.5p(IA)
