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Unformatted text preview: Math lﬂA—Examllﬂfﬂﬂl Name: 1111M "LE ‘éDLUTIDTJ 1.  1
Depusits t11 fund: $2,0ﬂ'l] paid on 11112011; $111111] en 1 1121117! Withdrawals frenl fund: Nun2 Interest accumulates at the fulluwing rates for the var uus periuds speciﬁed: 5 111121111 thruugh 12121121115: 11”“ = 3% ,
12 1111211111 thruugh 12131121121: i=1?" LI”. — 1 = 1.11:: ea 1' 
11 111121122 thruugh 121311211211: 11141 =e'11. What is value of the fund as'uf 1213112ﬂ3l'l? D11 the pr hiem whichever 111a},r ynu
want. If yuu use the W functions un your ealeulat , ﬁll in the buxes heluw. Bank I eredits interest at a enntinuuus rate that is a £11 etien of t: ﬁ[t}=.ﬂﬂf{1+.ﬂ3t} ggejLe 1:. Lﬂiegggge L a} $5,090 is depesited at #3. ‘What is the aeeumulat .d value at 17:? ? sham v me» We. : Sm I,+~o'i'>="l> itaiixl 1:} Mat neminal rate (if interest, compounded qua erlgorr that is earned
between t=3 and T DJ Alex herrews $3,I]Illll from Bank F at a nominal rate of interest 01' 8%
eempeunded quarterly. Twn years later, he pays F 96 ll. Three years after
that, he burrow another 5X. Fenryenrs after that. he ays F $4,0ﬂﬂ. After wltiell he still ewes the Bank $2,3ﬂ8.33.
e») X qe. + 45 (ememwﬁ) Caleulate X 35m 4: (m? rib q! Prejeet X requires an investment of $1,900 at t=ll. Th investment pays seen at
t=5 and $91“! at 1:212. Prejeet Y requires investments of $5M} at Fill and att 5. The investment pays
$1,100 at t=1 5. Prajeet X and Prejeet V has the same Net Present Val e [NPV], based an
annual effective interest rate i. {mm} Qt“ c‘l‘m a} Calculate i. )4 OPE: CI‘J Ft}? é:
Cable’s 41ers Basel a qt 3“ 1 Cl“ 77"? 5‘ :2.
cat: 6 : <tTet> Feta L
b} What is NPV}; — NPVY based on an annual effeetiv interest rate {If 6% IZCD‘A Elucf. g Wang and Huang eaeh burrowed an identical amnunt from Wang at a nominal
rate of discount {If 5.4% convertible quarterly. Wang repays her Inan by
making payments of 32,0011 at the end 0f each year fu l5 years. Huang makes
payments of 54,5111} at times 1T; 3T and HT. Solve fnr T QM: ‘i‘ié’3~‘e&
€451 2<Lhm> inlet
My = Cb HE'L Q¢4z<tgm>w¥ﬁ '1
IKK : New?“ ﬂ.  ;
Sports Manufacturing needs capital for expansion. It borrows ii? 1 £00,000 from
Venture Bank for three years at 6% nominal interest‘fc'onvertihle quarterly, and
$500,090 for ﬁve years from a private investor at a 5 an effective discount rate.
At the end of tvvo years, Sports Manufacturing ma s a $200,000 three—year
loan to its supplier of titanium {for baseball bats] at ‘33?) annual effective i nter— . est. What annual internal rate of return should Sports‘Manu Facturing report for
_ th_e__con1bined cashﬁows over the ﬁve~year period? ___... _.. _ . —.—_._ —— Values of Fund: Date 3mm ﬁﬂﬂﬂl W New 14.00“ Depesits: semen [mu 1}; sense (4”!!!) 15 um} Withdrawals $1,5ﬂ'l] (1 Hill); SISIJ {#2311} The dollarweighted rate ef return fer 2ﬂ11_ is 10%. What is the timenweighted rate of return for 21111? In year calculation, you can ignore the eﬂ’eet of one er days of timing differences. Also, fer dullerweighted ealeulatinn, you Jam use either simple er
eempuund interest. ' £3me (W
_ {MELX ¢ [m ‘Ls‘ﬁm
CF15: (WW?
em : {ﬁsh‘s Heel >4: l¥IOE?"le<i*l a “HAS. Prefesser K has retirement savings of $5ﬂ,ﬂﬂﬂ. He pla s to retire 2i] years frem
new (when he will he 9“ . He would like to reeeire $5, [Ilﬂ eaeh month far 15
years starting on his 90“ birthday. How much {lees h need to deposit inte a
savings aeenunt at the end at each quarter for the next 2!] years, assuming that
he can earn an effective interest rate [if 6% far the neat 35 years. Jeremy deposits $250 intn an account at the end of cac 3year pericd fer 3!}
years. The account credits interest at an annual effecﬁ e interest rate of f. The accumulated amount in the account at the end at 5 years is X and the
accumulated amuunt in the accuunt at the end uf 3!] ye rs is 4X. 3 Calculath M 11+ng1'13 it zwgﬁ ill]. At an annual effective interest rate of i, the PV today a a special Iiipayment
annuity is Still] Payments are made every 2 years and he ﬁrst payment is at t=ti.
The ﬁrst 5 payments are $11} each and the last 5 payme ts are Eli} each. Using the same annual effective interest rate i, ealenlat the PV of a perpetuity
that pays 35 every six Innaths1 1with the ﬁrst payment 2 years from ncvv. MIWM ._.,mn._'£aa . ...
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This note was uploaded on 04/09/2012 for the course MATH 172a taught by Professor Kong,l during the Fall '08 term at UCLA.
 Fall '08
 Kong,L
 Math

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