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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 ccntlznan}: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 12month 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. _. iiiMitﬁa _“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 ill1]. 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'ai Ladl" Liana“ .J
“mmus 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 25year annuityimmediate 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 5year 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“  __ ‘ "Nit 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 CamSe 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 lamchaise one of two annuitins: Annuity ]: A lDycar 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 intertat rate of i. the pressnt vain: ni‘ Annuity 2 is twice the. prnsnnt Dim vain: nf‘.Illtn.1n.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 Cum3:: .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:
13 @ 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: _ ..
lie1a 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 Ieam 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 liijlflLl) L m i L w WM vu K5; _
via:
1,0 (53 <97 ‘20 _ (a).
w ' W
at t‘'
i i _,. i1 L ant4+ __
—" {mien d) I rel. '_——— .
I 74:61 a: “Lem «men c FairsL SEW
w 5 ELYIO'U 3R3SQ3 ' my Maven: bar 2935 i F Cnnrse FM 45. A perpemityimmediate pays [Ell] per yea]: Immediately after the fifth payment,
the perpetuity is exchanged for a 25year mumimmediate that will pay X at the end of the ﬁrst yeaa'. Eath 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 perpetuityimmediate 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‘liyf A WW1“: Lari “tee/W (C) 13:: _,_"$_..+ if“)? it XCVDEQW [D] 140 LBﬁ" 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 — Bhi'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 Io‘s {as ‘1 1933 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. WWWJ1 @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 JalénaLLDur SCH—$3 ~
: KUﬁLClfiihm 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 > “SW7f 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 11) years. the account is wurth EQDDG . 1 D 112. SiLEﬂir I
Calculatak. (_Qﬁd ink3 E) :1: m
{A} 111 “:5 . hﬁgﬂgh
(3} 115 1 RS ($66: 44
(1:) 121 ‘1’
1 1" 11,
" :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.
 Winter '09
 kong

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