SOA #4 - ‘p (‘9 An insurance company has an obligation...

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Unformatted text preview: ‘p (‘9 An insurance company has an obligation to pay the medical costs for a claimant. Ayerage annual claims costs today are EEJJDD. and medical inflation is expected to be rte per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals. with the first claim payment to be made one year from today. Find the present yalue oi the obligation if the annual interest rate is 5%. h. a [q a; - PM... a Jedi $131932 {B}1D2.514 r W'flhi'é'7 ‘ 3" ME ._ (C}114.fi11 Hag , {a 1M, 1 {E} Cannot be determined I r"r~.i___ __ _ 'M’i: F I r- ———— —__.__ ———__—— _.____ .___— ——_— ' 7K3! p 9‘. A senior executive is offered a buyeut package by his cc-ntlznan}:I that will pay him a ninunthl},r benefit for the next it! years. Monthly benefits will remain censtant within each of the EU years. At the end of eaeh 12-month period, the rnnrnthlgtr benefits will be adjusted upwards to reflect the percentage increase in the lCPI . You are given: (i) The first mentth benefit is R and will be paid ane month fratn {ii} The CF] increases 3.2% per year forever. ' ‘ - At an annual effective interest rate at' ti'l'tti the buyout package has a value of 1130.000 . Calculate}? i“ -- - FL-.__?_M:F_ F' “Fe” ‘ 1?. . _ I I _IH- —~ I". I I "—— i __ - _ I (at an ‘1 ....:..;Ftie1% _ __ _fi____ "at g ' F (a) see 4i. _. iii-M-itfia _“E.i?_l‘b_i;_ tuna. ‘- r}: x i : t} 540 7*“ Hat! =1 4' Eli-(Es E) a M — "- (E) 563 Course 2 it} May Milt] ‘6 Matthew makes a series of payments at the beginning of each year For 2D years. The first payment is ill-1]. Each subsequent payment threugh the tenth year increases by 5% Treat the previous payment. Alter the tenth payment, each payment decreases by 5% from the previous payment. Calculate the present value of these payments at the time the first payment is made using an annual effectiire rate of 'F'Ve. (A) {C} {D} (E) November 299.5 I315 L335 1395 I405 I4l5 . . e . —J- In; L” pen: [flkwwtfi _ ~ ; L31 _ lfirfimlm L‘t'% END: 1WD! [D firm s_. 1 151} [ pagq’rcfi’i + Lrsgtfi‘e‘ls 4 l “3?; “file l - ID -—- .' ‘+ . Lg 't'a-i Lad-l" Liana“ .J “mm-us Kalli—1i- .93? “hut? brim i'°'i+ _ it NT— _ s " he ‘ Lo ? r “sustain trfia: it”, ‘ A, j 191.: !. Plr’lf l Fur ' 23. “The present value Ufa 25-year annuity-immediate with a firm payment of 251210 and "" ‘decreasing by 190 each year thcraafier is X. . } I 1 Assuming an annual cficctive internal rate 1:11" I 0%, calculate X. . I . m‘f. .{m 11,345 3 .113} 13,615 Um Lia I/II | 15,923 ' (D) 11,396 151 13,112 __._—'_.__—l———;———-—-- -- _ I ant—H- ' j 1*; 11:1 | +1 ; CF _- | ——-I- i : "15"", ' K111 “=1 1‘5“le _ November Elli-‘35 26 61722 Course FM 69 b i6; Olga buys a 5-year increasing annuityF 1‘an . Olga will receive 2 at the end. of the first month, 4 at the end of the second month, and for each month thereafter the 'pnynient increases by 2 . The nominal interest rate is 9% convertible quarterly. 2.1” CalculateX . a. W Lu _|1___ m IPMT IFV _ JEE‘id__ I | {A} 268.0 we I i I i I a A: = _ I I @ 1T3“ | __ ‘ "Ni-t- i — . h— r H y {c} 213:] 5 ; __ ‘ “a ‘ I I 3 tea I_ . <1? i is}; I E {n} 233:} i-‘fl'fltfifl xii-“3:1 1,362.3 {E} 2330 U _ - LE 2 Cam-Se 2, November 2190! I 0/ I 9. The present value 01' 3 series of St} payments Starting at 101:] at the end of the first year and. increasing by 1 each year thereafier is equal to X. The annual effective rate 01" interest is 9%. CaieuiateX. [my to l “J I f = CLQ e 3 OH : - r {A} 1165 At 1 2.. '5. (B) use .1 1195 ‘H 0t 371 T Iaga I {E} 1225 fl 3:. -— _ . — i ‘—-~— .' ——1.— +——— —- 3'1) I ‘fi ' Ki I' <J P ; ‘33 g —— ———-——-— ————'—_— I . . —_—— _______ _____ ___ __ ____— —___ Course FM May E’flfij —.___:.....- I' 44. It): can lam-chaise one of two annuitins: Annuity ]: A lD-ycar decreasing aimuityviinnmdiatn, with annual pammm nflfi,9,3,....1. Annuity 2: A pnrpehfltyhimmedinte with anmml payrncnts. The perpennty pays 1 in yearl,2i.nyea:2.3inyear3,...,and ll inynarll . Afinrynarll.flie payments remain constant at 1 1 . At an nrmnn] affective inter-tat rate of i. the pressnt vain: ni‘ Annuity 2 is twice the. prnsnnt Dim vain: nf‘.Illtn.1-n.1ii::,ur l . "i u l' Calculate'thn value nfflmuity J; 1 l l a D 6:“ m fl (A) 35.4 Hana -Dnm : in Dar; [3)- 3” it ~ "w— (L (C) 33.4 1 3* 39“ _ a m : (an? (B) 449.4 ‘ FL_II_EMT__.L_EL | _ to i TfiMMHLL L _____—___—__———___—____________________—____ aw Cum-3:: .7 #4 _ Form (103 12. A pflrpfltujt)’ coats 1'11 and makes annual payments at the end of the year. Theperpetuitypays l ntthe endefyear2,2at the mdnfyear 3,..., n at theend nfyear (ml). After year (n+1), the payments remain constant at n. The annual effective interest rate is 113.5%. Calculate n. L l ,g k; m '1"; Vi _ - - [W'l+l"' “ {A)1?Gju,i_g\t-~nwim-, , {B} 18 _ D <0 (a) it“? - r e a (4 (D) it} “7 Mia—n?! link . (E) 21 _ “HI 'Ifltfl: 1.. [Q -—) 1) Inga ’L’ 1,1 (‘1- mm“ (#53. - 7} l l L ’0“: 1: =12 “w *- [5} n j__t I _'_ 3"}. i L .S': ..- I ,«i- I { I I: I Ch - 1 t3. t . ' ' :2... w May 2W3 25 9 “3‘32 2 @969 26. - 10th] is deposited into Fund X. which earns an annual effective rate of 6%. At the end of each year, the interest earned plus an additional mt} is withdrawn fiern the fiend. At the end of the tenth year, the fund is depleted. The annual wifiidrawnls of interest and principal are deposited into Fund Y, which earns an annual effective rate of 9%.. Determine the accumulated value of Fund Y at the end efyear 111' [truth [A] 1519 J» ‘r 'v' 1__t.—e———’——i K {n} 1319 a, , ‘L e - s ' 1-:- 1-3 @ mm high is; fl 1 big it {D} 2272. l g. ' “ v (E) 243] 6 May 2003 29 arse 2 Course 2, Neveruber 23W 35. At time t = fl, Sebastian invests 2am in a fund earning 3% convertible quarterly, (Leg, 9: l :‘Efi‘wg ® 1 m = {Mae He reinveats each interen payment in individual separate fluids eaeh earning 9% but payable annually. convertible quarterly, but payable a1u1ua]ly.( I“ D “53“? _ i 1 «L3? itfl y: _ .. lie-1a Hafiz-‘3 The interest payments from the separate fimrls are accumulated in a side fund that guarantees an annual effective rate of T‘Ve. Determine the tutal value of all funds att = ll} . ' a 1m I Ill’ u A ' f {A} 3549 l (B) 3954 latent with his“ % If “I (C) 4339 LL i leaflet: I D {D} 4395 13' tsxfi ' “th “C” ea [Sislafi * (HOG! | l | in Ll 5" cm 7 l j . re _ a. Sea ‘ I l __: ___|“ Fess—u M. ""— \ TM :- ‘2em e image. 3339, e we}? 13": . 14. II Payments qu are made at the beginning of each year fnr 213 years. These payments .u I II I-eam interest at the entl nfeaeh year at an annual effective rate of 3%. The interest is ' i itnmediately reinvested at an annual effective rate ef6%. At the end efli} years, the aeeumulatetl value of the 2’0 payments and the reinvested interest is 5660. W K = EI' u a i ' 'ta 0 jCalculateX. $.50 film film - “'3‘” .Im) 121:5? {i L ‘L “\A Z- 2356 15% in? I E I F _ E_ it: fiifinfi .(C) 125.12 -' Eb M $ in} 12?.l3 . I: E) lease ~t ED" .9 ‘33 liijlflL-l) L m i L w WM vu K5; _ via: 1,0 (53 <97 ‘20 _ (a). w ' W at t‘-'- i i _,.- i1 L ant-4+ __ —" {mien d) I rel. '_——— . I 74:61 a: “Lem «men c Fairs-L SEW w 5 ELYIO'U 3R3SQ3 ' my Maven: bar 2935 i F Cnnrse FM 45. A perpemity-immediate pays [Ell] per yea]: Immediately after the fifth payment, the perpetuity is exchanged for a 25-year mum-immediate that will pay X at the end of the first yeaa'. Eat-h subsequent annual payment will be 8% greater than the preceding payment. Innnediately after the lIZII11 payment of the ljryear annuity, the annuity will be exchanged for a perpetuity-immediate paying 1’ per year. The annual effective rate of interest is 3%. {are New: -— Leflqu: fl =I,1ro CalculateY. . I (A) 110 ‘ (Bl 12a [PdQ‘liy-f A WW1“: Lari “tee/W (C) 13:: _,_"$_..+ if“)? it XCVDEQW [D] 140 L-Bfi" l 3&1: {E} 15D '— ‘x: “3* ,— ..__ t. - 1.3 lbtc'lfhkh“ at max 15' [affix/z {giro :2) Kygq Cuurse 2 —_—______ I I_ 1+ ‘XCtuQD +3<Cw§3r+ _ + )5 (HQ) i than)“ l0ng lash”.- flg — Bh-i'JT‘gE LIT—1': I, 9. November .2995 A companyr deposits 1003 at the beginning of the first year and fill at the beginning of ' 'i If each Subsequent year into perpetuity. u 1 {in return the eompan}r receives payments at the end of each year forever. The first payment is 100. Each subsequent payment increases by 5%. Calculate the company‘s yield rate for this transaction. (lo we) figs-‘32:: I2 Cf, Course FM {A} 4.1% [cm to} 5.1% (0‘00 4- {Scam : tfibfi + A; fit?% g M MW _- to) 11% E fie - i i Ste C { HT arr—['03 3 ' if“ tart * (git? gunf- “ r im I-o‘s {as ‘1 1-933 f w; i {we} 3 :- it"? 3 -t 'fi {.1- _ i — 1m '____x___— _ 11:10 b ’__-' ' ‘ Pr? ( Lme‘f‘) 1J5 (‘11:; _ _ Q—Qg'l [W e m3 4; " 3 j _——-"“ __ [- W3 :l: ..e _ _--~ I __ Victor invaa a bank account at the beginning of Each year for 2|] years. The account pays out interest at the and of awry year at an annual affective interest rate )9; . 33mm on the antim- investment over the 20 year pefiod is 3% annual effective. WWW-J1 @141: 2C" . . . i of We. . The interest 15 mnvestad at an annual efiactwc late 01' [— 2 This DWELL—fi ‘ :L ‘ Ed’ Pvtfr g: x v '10 Q. 05 Q5 ‘1‘?) at k" 3 (A) 9% l—‘F I LEW??? _ (B) ID‘E: 1 u (c) 11% O A” —- fi’fiirflx'm: 316m {B} 1124: I {E} 13% it E fl , wq 19. .‘7 EEHLELai—a Jaléna-LLD-ur SCH—$3 ~ : KUfiLCl-fiihm m 1‘ . 4.. 'L 3 L3: (1% -s; u =laa‘ fig“ " _, ~ wimmv LC 13L ESE/(Hz) (1572;) :: “(L I __ “3” ‘7 ' 73° ___\_=: WLELE L—- 65:53.“:— N “1/1; 1—” CARY—é % 3' 5 in = 1%”? J __‘r"~ ' A. '_r_g'_| m Lax? _m If. (i C t > “SW-7f HS I 2% Payments are made to an account at a continuous rate of (3!: + 1k), where '0 S 1' 5 ll} . 1 Interest is credited at a force of interest 5, = —-—. 8+1 Aflar 1-1) years. the account is wurth EQDDG . 1 D 112-. SiLEflir I Calculatak. (_Qfid ink-3 E) :1: m {A} 111 “:5 . hfigflgh (3} 11-5 1 RS ($66: 44 (1:) 121 ‘1’ 1 1" 1-1, " :1: * 1 Smmfi 1* ___—___ __ __ __ __ __ _ _— _ Course 2', Navemfier 2191?} w w ...
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This note was uploaded on 03/02/2012 for the course MATH 172 taught by Professor Kong during the Winter '09 term at UCLA.

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SOA #4 - ‘p (‘9 An insurance company has an obligation...

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