Quiz3Sol

# Quiz3Sol - ACTSC 231 Winter 2009 1[8 marks A certain fund...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 By August 1, 2009, the fund’s value is \$27,500 and \$3,000 is withdrawn.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 L00 (1 a)“ l _, .. "T , + “1000(291) L ~3 .3. . r1 : - ‘tOOC \l ZS 00C» (1 +13 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 time-weighted 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 ,iv-l : 13.76151 (d) [1 mark] Why do we use time-weighted 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 lV‘CK A Q W CC‘k pave—M l , ‘in’x S 1: U‘l H‘Vz‘i. ‘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 n . y(c {sis-(777) :> ‘v < Miser-1 => e S; :l lJLJé/l Fay) 3 ’Flv 3 l s‘owalbr : Fwd Q 5 b 3 (j t be : 54‘ CK‘ﬂ 1“ Q \/ :> b2 1 35 3 l U‘ d 2 (b) [2 marks] Calculate the outstanding balance at time 6 using BOTH the retro- spective and prospective methods. .6 Ralw: OLYUG L leOUiOS) ~- GUS—'3 :iii?\2.7? ’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 ’l' T in} m (b) marks] A monthly armuity-immediate 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:- NUriiM/UI) \v'\ WAWS‘} L -‘ " ) l” ' L ‘3 ‘1 __ ‘_ 5e l 54"]:1 to»; H730 I ")"""SS L r’. \$1 W '. i) v“ AV _ 1‘ {— LUU<bt¢> T ~ ~ 1" 3v; ; ¥O + l0 (IS->53 . . sK » 3? 1..*3€' . a... : ‘7ovl\+\) “ I+ [O‘q‘ytfc‘ CA3] . t t : L[l <5 l C] . l O (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 ' . §_ , m r '9’ TEN : ibou \( + luvl l53)V + luv“? (‘ (’7) V f _ 100:; t/ _ lQJC {0‘3"“57’ l‘”\‘~'/\$\l Hr— 0“ {‘0“3 3C] (1 K \V k] .lrc *4 [Jade] J WLMKLk ’5 leitdr _ lgb' I L _ :7 (k ._ Q 073) L,QK]\]\?)/(; : ]DC/OC ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

Quiz3Sol - ACTSC 231 Winter 2009 1[8 marks A certain fund...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online