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

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

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3
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 By August 1, 2009, the fund’s value is $27,500 and $3,000 is withdrawn.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

Page1 / 3

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

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online