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Unformatted text preview: ACTSC 231 Winter 2009 1. [8 marks] A certain fund begins with a value on January 1, 2009 of $23,000. By May
1, 2009, it has grown to $25,000 and a cashﬂow of $4,000 is added. By August 1,
2009, the fund’s value is $27,500 and $3,000 is withdrawn. Finally, at January 1,
2010, the fund’s value is $28,000. Assume each month is 1/ 12th of a year. (a) [1 mark] Set up (but do not solve!) the equation that would allow you to
calculate the exact dollar—weighted yield for this fund over the year. 3 2
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13C 150 m + 533% v“ + Zfioou Ox, (b) [4 marks] Evaluate the dollar—weighted rate of return using the following ap—
1,)roxirnations and circle which one would be closer to the true value. i. The simple interest approximation j: :2 23%; ‘ 13:19:) ‘ (‘1003 »~ gave») ~r “(m .r AM) a I Liege + .. ii. The midpoint rule i M 145 _ 2 X‘tva
$0 + Jr\  l: 2330;; t 25500:: ‘dbb 3 11.02470 (c) [2 marks] Calculate the timeweighted rate of return for this fund over the year. a {‘1 . 1+1, 2 : Lofﬂ'fi/O J" I": l“ k; i : 0 '7‘1’ 732.57
‘53. ~31 1w e 2:33,; ~. : Mme:
7’ = “Hui/1+1.ka ,ivl : 13.76151 (d) [1 mark] Why do we use timeweighted rather than dollar—weighted rates when
measuring actual fund performance? Explain in one or two sentences. V38. use L‘WQ.”\\I‘€.;(Ol¢‘l€A heCC/‘k/USC FQMQVES 1 He 0. c} o C‘Cu S‘LK l o u) .3 Lv la L: (A flu; aft/de
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‘2 C 0);», iv C 3.9 i)" lufxci > (uL vvlﬁE/Vk OPE Vukc’n, (‘4 m Ci ()y ~ '7 \3031‘4 S /V\/\ d/(chml i ‘34” F ’v'LA/YL AC} r \ luv ea 15" ACTSC 231 Winter 2009 2. [6 marks] A loan of $6,100 is being repaid by level payments of $950 at the end of
each year, plus one additional smaller payment one year alter the last level payment.
The interest rate on the loan is 5% per year. (a) [2 marks] Find the number of payments and the amount of the ﬁnal payment. We wt:th ClSCQn—rn < 6ND é CiS‘O gm ‘15:; 0.05 ‘ M
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(b) [2 marks] Calculate the outstanding balance at time 6 using BOTH the retro
spective and prospective methods. .6
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’Pm: OLEG : qsoiv + stinks:va 451%??? (C) [2 marks] If instead, the loan were being repaid by the sinking fund J'nethod
over the same time period but with the sinking fund earning; 4% per year} wllat
would the total (level) annual payments be? int—641234 : DC) 7K “370 305
3t hepsn’l’ \3 T" (5f élOy — gig—17% ACTSC 231 Winter 2009 3. [6 marks] Annuities/Perpetuities (a) [1 mark] Draw arrows on the timeline below that represent tl 1e times when the
given stream of casliﬂow has value 3'3] + fig] (ii) Hag]. 5'1 :31 $i 3:1" in
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(b) marks] A monthly armuityimmediate starts with a payment of $80 and pay— ments increase by $10 thereafter. Find the acctunulated value of this the end of 3 years using an interest rate convertible monthly of 6% _ _ V Rim—7w"
(but do not have to) use the formula ([0,)m : annuity at
i You may . . , ‘ (5‘7:
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(c) [2 marks] A perpetuity with payments increasing by 3% per year, with tl payment $1,000 at the end of this year, is purchased for the same price as a level
perpetuity paying $2,044.86 at the end of each year. Find the interest rate. ie ﬁrst lbw i»"(\~=‘>l l:.;¥‘"l—“‘>)L '
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 Fall '09
 Chisholm
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