保险精算课后习题答案

1、2.1解：(i)根裾题«，得zf/=5000( i +ff)«5000( l + io%x4_5000( 1 +40%>-7000(元(2) .4r=5ooo(l+o-5000(1 +8%) »5000x 1.39538 = 6976.9(元) (r按年人榭汁 hio joood+o 5o(xxi+8%) = 5000x139536 = 6976.8(ju) (f按夫数计筲)22解：4/=5(mxx 1 +8%) 1 +11 % f -5000 x 1.4693x 1.6851，12607.08(元)23p = 10000(-)4 =10000(1)4 =

2、10000x0.92594 =7349(元> 1+i1+8%(2) p = 100(xx1 -11 %)4 = 10000 x 0.894 = 100(x)x0.6274 = 6274(元)2.4i1000(1+z) =1200./.!+/= 1.44,< = 0.44.即= 2(vl+7-1) = 2("1 + 0.44-l) = 0.4，in aado> = ()' = (r - 0.30561 = 0.0285. l+i 1 + 0.4425证明:vf=(i+r-itj=i-(i-r,广 =(i/«>! 时，两边収极限得i-lnd+0

3、+ -2 而 d = ln(i +/)/ -1 = /， i-d>0. w得iie<z«r"> <d<i <i.2.6证恥(1)左怂=tf =lzill = v*-(4r+i+i + v)= v"(4- + l)/7 + v"(l 十 v*)/ = a-+ v"a-=右边。(2;左边 a - =v(l-v,'-)/(|-v) = - ”"*1-v=vv'w'-f1 :v(l + v” i vo_v_w) i - vi-vi -v卜v卜丄il+i-v .s:=心边.=5-+(!

4、+；)" 5 =右边.(4)左边-sn = £±!)12sl=(i+/r(i+/)-'-1/；-弋(1+'»么边.2.7解淞据娌总，得3905(1+12%)20+3005=,330x13.947 lx 9.6463 +300x 80.7311 = 7.4683j , v_(4036l.37 + 24219.33)/x=/7.4683=864731(元)l|j毎年末可以领m 8647.31元.2.8峤:根据®息,列式如k5000么=xa-,5000.鮮忐-19769.4 （元）即毎次能够提取的域人金输力19769.4元.ill:明

5、：a:ii» a =左辺 5；=心边.240解：(200 + 100)/(l + f) + 1000.i d-v)(1+/)/；nv 112%= 1200 + 100()戶 + f) +1 _ x= 19643+8333.3=10297.6(元)习题三3.1xpt1000010000011000.98911198900494.50.9955248405.5295.2160.99733.2otm 0 + 0698ro = ;=(5,0< + 06,oe=tia» ()= ()000001 liki ()='/ 叉-06铐*沭唞孓v* 4m0=>fe (z)

6、x + ()6、 mx)0000l= /场妒矽山佃-06-»fua* a (xioooh7 = (|t5 1000001 肋 00(肿=力(i) :i» rf弘 (-1)0001or!=穴)=/ on (i-ooooion 、-itoooiv 二(n1-(77-1)0001'>f ,021 x(-1)0001d= 03107j=(>>oc06 (涅-咖8co=6zc8 = (¥ -1)0001-( -1)0001= m/ 'v = '尸 tnito = ( -do(m)i= 70001 = (十-1)000卜，(i)0 0

7、00900ori03190to081ooff0sooof009£ro8.0os i(lz£1.0£8.00s10061ro60000100010'brd戶77一乎剛口-o/l00ch）砌825（1）址明：左边x岁的人/t xn-xm岁之m死广的賊率艺丁 .v岁的人沾刊岁的槪率« ±x岁活到rivi+m岁的槪率左边=jt = -npf q=右边 ". r 11 i概g ； . i'- ,，.,岁的人a i+n岁之间死亡的槪率v岁的人存活rrnr年的槪4t$ 丁 y岁的士疗到x+zr岁的t苻槪宇乘以# «岁的人生

8、存判 十m岁的生存槪申（2）左边=书、是，=-平=1 =右边3.«（3）左边：4今今今卜pap，-p，j =右边（4）心边-f.（-解：死亡均匀分布假定如卜:（i）w45i 4o-d;a45>=0.01798光亡力饱龙假定如卜: （1）l-e *. = * (ln/；4 -ln/,ft)= lni78 = ().(xk)3p45 = |lnk】 =去 in 卜.=0,63.84.爪=匕 =漏 °f3i4o定下:.= = 0.0003 4】-(卜卜(2) / .=91466.20,4 |1 (2+-2)5，= ； = 0.0179 z4oy40 = = - = 0.00

9、39. 40-；00839= 0.00841- x0.008394« 0.008444l-(l-o<7404di (-i000 >/l00-x)7 .40-铸',=1 =' ！ = 0.00836*1000.ji 00-40iie 阶介 fis 兑兆規怍卜介.v( x) = i-,hp/t= /o(i-), ww7-=.<.|=右边. .r*l3.11 解 ptahxrc-士习题四4.1w: 11.明木f j: 2000818a,0 = 2000 糾；= 6928.308(儿) d|0n - j(2)期 fffj: 2000818a0 = 2000-

10、' * = 7352(7c)心边.方法二l=vptl.£dr li d由一诘、厂之|得证.祕左岭=|今211. i±l = 1 + vla±l . v 乂= l + vpath =右边 方s-:证明：fl -、c +、d'j dtdvpd:“=1+< =丨+«,=右边(3)证明，左边=1 + £氏-1 + t，£r -ne. = /f,+(l-ner) a一 + (1 n)er /=lralr«l-桃(4>iie明：左 14= wlar = nex .a、.” =、， n =右i2la/ -/v证

11、明：左边=(6»w pk xdr=-a =(i + /)n,4j解：a®年给w 12* a；.7-150000=12+ p)解 w a=3 丨 8.44(元)4.4解:己知s月给fl 200元,则一年付2400元.60岁幵始，10年定期的1年12次给付a即诊年金现ffih 2400x-10 a)a, i = vrt-p,dt = vt(-tq()dt = v 1, f v i、二<7().in v in r (in vpv=，lnv = -(m-v = a. 质式:ko)4.7佥觖年份1000 1500 2000 2500 5000 4000 3000 2000 10

12、00r x+lx+2 r+3 x+4 x+9xlo.rhl xl2.v+13根裾转换闲数.可以衷示为1000«+ 500(/,);十鵬上以.4.8w： a=jv;c,对一切x有 -(1 + r).up /*=(!f=(|+ry/；4以 i 和/呔础，=fjv'y(l + rf <=i以r = $ 和p:力基础， = e(-fr7)f=t-(i+ry /-i 1 -1_f. 戶|第h:章1卿-士)，保昤的ft党现ffi 1 (>0(x)0 =100000? ' ，屢0 loooooy'/m"j知：气ra65 时.tp = 0.'i.

13、 1000004 = 100000各（土10000065 lio = 15353.24（元） i4；i.io53w： /i年过明舒給精w现值鏵人,n年延期na年定期寿险:kworiak =10000= ioo（m）（> = 402.54（兀）1069.6405-403.724916542.86_ ax=vqx+xpyaxi 边v+%jv'l.4+ir+l卜今1=7 «-lv，+i）令r十i.则原式 r.（uv + jxd十v.（rs fm）今t=t.则原式=4h卜05.7.v = i 1+i(i +av)-ox 1+/l + av加az吾1 = _第六章6.11210.

14、195720(x)0x0.018772 =3 75.44(元)久 64467.45-27664.55 - () (b2ss320wxu,0328s3-657.66(7c)狄：1 ooojm,+ (j57醐)io年限屻缴费的卬噃冲保贤为p娴p保险费埂«£力pa d3c(-100(x)mjo + 5(x)0/(1 + /)'° .dlc)么=1636.48(元)则194.46/12= 16.205( >l)6.4= 0.028421解：弋 =0.023308则 a = 0.c29387w f 为：3000/4 x c = 220.40(元)肪7.45;4 = 219.364(元)=0.028421= 0.023308则 =0 02938730(xk)r4x- = 220.40(jl)6.5乂«.n，f若氏+as，= a；.則原au r =4/ 5 =艺人k+d.sx = ±tmx，r+d.n",)-z(zv<_)r=0既淋证第七章0.0875=(厂”則ojo-io - 40j0404|050ma(1.4) ( = 1429.9113=va=,l29'8f)4u = 1029.22( 7t)h： f .- i mt _