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# 172C - Math ITZC Mid-Term Exam-— ENE Name LG 1 Fm a...

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Unformatted text preview: Math ITZC - Mid-Term Exam -— ENE]!!! Name: LG 1. Fm: a special 2|] year term life insurance pulley issued tn {it} ‘Wiﬂ'l level annual premium payable nvet the term 01' the policy and death Ileneﬁtﬂ payable at the end nfyear of death, the tntal death heneﬁt in equal In \$lﬂ,l]llﬂ plna the terminal reserve at ﬂte end of the year of death. :13: .02 for all x , i=6% Calculate the net annual premium. _ (mail Magnet“ -¢¢M. M1 QU+F§€1+L§ :‘ Colgt”—t+1V)1ME+-EHU (a + {33 (but) : CLnretnd-ﬁNH Nan-e1 -{‘_ LV LU -”- PC'caED— L50 C PCl-DQFW + 2‘”) (we) : Clam-IE1“ LU ~J)ﬁ~n2 1“ LV L“: «IKHQ‘LK'LW‘ME‘GED—Hg 121V 3 PSm —2,51)Sm “V : Pgﬁelﬁﬂgﬁ—l l. 1 ‘l’ 3m “e 95.774 CHE) P: in? : {R57 PM.) a..—___,_____h -=_--—_1 aha 2. L is the lose 1: issue random variable [er a fully discrete mediﬁed whale life insurance pnliqa issued In (x) Net preminma and death beneﬁm are as fnllewa: Ye ar Premium Death beneﬁt 1 .5P \$50G 2 .TEP \$751] 3+ P \$1,ﬂll}l] P=\$4L932 <5?— ELM-Jﬁ't W Z ‘DLt-ﬁiz ‘32: .DZ, (1,“: .03 _ 2 . n M ir— Ari-H. 1%,.43930 amzaaaaa 1 = rm a H1 7. d Calculate the Variance of L (Hint: what is the 1Variance eE 2LE") LL ‘2 Lrﬁ-Blc 1 + WET; ghegl 61361.], F “WET—3 7" [13,111 (ﬁriLn—ﬂm—EJCMQ =Eﬂm mun-ﬁg a [U —_‘-;) N 2114715; .153 (Jpn-ED: 130mm 3% we: 1v :1an ./ : 3.3m? ClL—‘t‘ll‘H—‘H-ﬂﬂh NM: 1m Am. - CHMH'i-tiei’] : arterial 1. ~ 7 : 15e-1.\$-E.M) _1>,,.¢[ 1- cl .3 [LﬁJHL g IIL‘ L L-né F a 1 PUB} '3' 11.30%?) a I arm-12W Mu ”Ht c” “M‘DU L, C r1. :Ir #9 H [43(3- {B16 5 {1%}?!er M A special last snnrhror annuity is payable to at the beginning oi each year to X. Y and Z in the following manner: If all three are olive: senonmx LC W ﬁ’PWL‘J W monomer 3 rm mm: W 56,1100 III .7... J, Velmgﬁ Len—ea. iii-ﬁe. mew—w If any oi" the participants die, their portion 01' the onnu _will he dnritletl ecpmllf;r among the survivors. £12511, ill.=1'|]; 533:3 57.3.59; iixﬁ’i"; ii}.,,=ﬁ ﬁgyz=5 Calculate the APV ol'1he total annuiq' lHl'BJcD : rm :9 b=éer<l}rm> A+Q+C+D+ETE "HR:— llﬁ‘m =3 G: [gig-pa Agni"; 1m (iii—{Lif-R-ql-jeé +3} I—_. — lséim The normal redrerneut beneﬁt in: Smith, age 65 ie \$1,ﬂﬂ'ﬂ monthly payable as a single life atmuity. If she eleeta the Joint and 50% Survivn: atmnity form with her apt-use, also age 65, the amntmt wnuld be tedueed be \$95!}. 1What wenld be the initial amount payable under the Iniut 3r. 66.7% Survivor with “pop—up”. (i.e., if Smith’a husband dies before her, the monthly ammmtwill revert hack to 51,0013) (x) and (y) are independent lives. A Special whole life inanranee pays a death beneﬁt of \$1ﬂﬂ,ﬂﬂl} at the moment of death 01" (3;) but only if [v] dies more than 11) years after the death of (x) tux: .03 p1,: .04 ﬁ= .06 What is the APV ﬂfthia insurance? .4:- L91 K M m'“ Li CL~ t34e mm x (3 EH ' “M W 9" I? "Guru? “3 Dgt _-cc{rt 8 &1 h (f a ﬁ‘ " III) F. to _lrt NB welt C-EHLQHTL ,, C .uwe + e, w E’— E0 1-D q; _.: at #— ﬂ _1 “‘5 — ‘15. E: Lg 8/ Dxfi'i '— 6, twp 4-3 If) :9 :6 Frank-P --—-———?‘D\P 1 «03—335 1 ‘l1 x lirﬂfw e-32Té 6. Complete the ﬁrst mm ram 0f the Multiple Dccremenl: Table For a dnuble decrement table, you are given: '13,”):3 'zlxam=*3 I H E") L" ‘ %F-q 7- ‘36 Decremenﬂ; fallawthc M'UDD aaaumption L1.) .— .. 73: ' W at m 15%” {*3 m ei Irv-3 111:) M32 L: eh ___I:'. :1 x Hm .. mac-.1 two 1+1 3:; 8 W WU “2°: ,cﬁ CD ,5. '- — : €36 cf) cw": - {)K —> in 9,"? 7 ,1: chﬁ ” 1,70 '13 F) lsﬁle'm 1£KZTD'€7:é7g L15} 9“,“; “ ‘13:. mm-r-ZYYS'EQ : S3? C3 ,% tﬁ _ 61M 7 “A "rim: _ 1 ‘07603 A population is subject to three causes of decrement, decrement (1) cccnrr. nniInnnly throng-h the year, decrement [2) occurs only at the end of the year, half of decrement (3) cccnrs uniformly between t=.3 and 12.5 and the other half, Ly ‘ 1 uniformly between 1:3 and |.=.9 a, A: ‘ 1“ W me. am an act - rm qt =-1;qx =1“: =43 a? x «a - 5: - v ' ' CHICﬂlBtE [lying {Item} 1 Elia} cpl £BL1' .: \ﬂ‘ﬁrh)‘: [_ thj’ﬁ’h—lﬁkg‘) : J7 Q, 164}: 062..) [3 0&4) + ‘10—‘15 Elf“) + ~1C L ,— +3 govt?) 5%“): {Li} Cacti“ + Jict ... 13m) Mania“) ”Fig“? A 3-state Markov chain is used to model the three mnditious of an insured: State U : alive and active State 1 : alive and disabled 5111: 2: dead Tmnsitions occur at the middle oftdcycsrand the Transition Match-t is: .35 ,1I] .115 .15 35 .10 I] [I 1 A special 3 year term insurance beneﬁts of \$lﬂﬂ,l}ﬂﬂ is payable at the moment of death to an insured who dies while active. How-wet, for art insuredmho is disabled1 the death beneﬁt is only 55D,ﬂﬂﬂ An insured is in state I] at t=ﬂ, what is the probability that a \$Eﬂ,ﬂﬂﬂ death beneﬁt will he paid during the 3rd policy year? 1G. Uning the darn from # 9, ealeulate the expense-leaded preminm5 for the special three year term Insurance for an insured in slate U at time 01' issue. {there i5 ne- premium waiver beneﬁts) The expenal: meta: i5:C [:113 E2“ :EE]+C:::::1j-LE [5—0 MW '2. Feet I C, LPLEt-Iﬂ': [Erik ms 4%! {PM Ti C [*f’ é‘EFCI-ﬁl: + C‘TITTLLLE) : 1-6011— 7; 49 U (1m :2 hp CleBBC, Leif-\$7??? [£231 .513") C c} ‘2: 3 Q1733“? (.131?~16'[n10¢.=§ f 3 33““??? §m%~\$:\$ + air-7:55" 5 Leah? pen; . biz-{11\$ we“: “‘- larcmﬁ’) (A (31:50.37 2:63“?! 3 ,x—He ...
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172C - Math ITZC Mid-Term Exam-— ENE Name LG 1 Fm a...

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