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# Quiz2Solupdated - ACTSC 231 Fall 2009 1[9 marks A certain...

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Unformatted text preview: ACTSC 231 Fall 2009 1. [9, marks] A certain fund begins with a value on January 1, 2009 of \$33,000. By April 1, 2009, it has grown to \$36,000 and a cashﬁow of \$3,000 is added. By August 1, 2009, the fund’s value is \$40,000 and \$5,000 is withdrawn. Finally, at January 1, 2010, the fund’s value is \$38,000. Assume each month is 1/12th of a year. (a) [2 marks] 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. Would this be the unique yield rate in this situation? Why or why not? ‘ - a A 301» L art” {If/’2" 7 r "‘ F) V ”.23ng???) -\ 350V V )vv —’ V ,r: J 3&9 ~ (1, f . V12. "3/1)- w Bissau“) « enmﬂhi ~ swam-w) 3mm» Rid? ‘2' 4AM?» V31 (i \ci (0K +5.. ”mix-J ] I] 5,961 \A/‘J; (ll/“EN: I7 {1 mgu ,S‘ «x? ‘ I L. - . ‘ . 9‘ ?z-.~ ~ ‘z-ax‘o “‘31; “,0 “S"?Qe‘ag 1&2. {x2 (:3 f (in, i (AA/VA 5‘ Upﬂ Z 4’ 9““) 4 '3 J I ‘ 5' i ' ’l ("I ,t 4,. ﬁx" 1' , xvi/walk ll‘kQ-Kixfe. (pi/LLL3 .L. «IVVXV‘J’: 0‘ . 5 ’] \~ (b) [4 marks] Evaluate the dollar-weighted rate of return using the following ap— proximations and circle which one would be closer to the true value. i. The simple interest approximation 1 S W 03 (7 L} O l W UV (/ Q » i i (“k3 )2 v r \. \ V «1 r) K, A \. (c) [2 marks] Suppose instead of \$5000, \$X is withdrawn on Aug 1. What must X be if the time-weighted rate of return for this fund is 25%? : . ix .. ._ "g 5 go 0 7 Ho Us; ~ '5 ‘5 0;.- m - a me» ~ “RA ' ] Jr g i ( . Mm. »»»»» m ‘7'“ ~~~~~~~~~~ .. -~-_ --------- m_ : hm" V J " , % 5 3w 59* ,, E‘ic m; ,‘—m 05'; ~ 7\ a r L 1 - ‘ . «V C" "J Mild-w???) 3/") ACTSC 231 Fall 2009 2. [7 marks] Alice and Steve have just had a baby Lillian. They wish to put a lump sum of \$Y into an account at birth so that Lillian will be able to withdraw \$10,000 on each of her 18th, 19th, 20th, and 21st birthdays. The interest rate is 6% effective. (a) [2 marks] Find Y. 1% m ‘ ('1' r'\ \2\ 1 \1 1 lb, » O x m , \g l .23..-. 33“ . 1 ’ -»—-—~ 1,.“ 13‘9““ \ C‘ Q] l ]O / \J<../ > 3’6”. > not ‘ (b) [2 marks] If instead of paying all the rnoney right now, they wish to make contributions of EEO at the end of each quarter for 18 years, ﬁnd G. Ll i313 03 .13, r. C @335 WWW (Hill) .—_- pct: ﬂ 1 / ‘LIM‘ﬁ‘L ] r c \‘l C l 1' (w iM] Pr 3.1.. i : Cr L42] 7}?” 1 615 C, ’4 2:]0 r L», :5 (c) [3 marks] Suppose the interest rate is 4% convertible quarterly for the ﬁrst 18 years and 6% annual effective after that. Recalculate Y and C. .. ”i :rls w v«,_~ \ ' :1 xi ‘1; ,1: 7‘31] , lQIJLU C/KQWC'jlil] inane; \/ "~ 1"” \“i a. Li 2m 2- l 3‘ (‘l L] 2. . S 2_ : C. 013;] 1% 1l ACTSC 231 Fall 2009 3. [3 marks] Basic annuities/perpetuities . . L = L ’ (a) [2 marks] Prove that am 5m + z 3&3 ~ "I" i a ‘37“; h 2 r y A; I’HEYLl ﬂ \_ _\‘\ {MARI \ , t : NEW" : WW “ L» 3 '93 !**v“‘ 0m (b) [Emarks] A wealthy UW alum leaves money to UW in his will. He wants half the present value to pay for a new building which will cost \$300,000 at the start of the next 4 years, and half to start an endowment which will pay \$P at the start of each term (1/3 year) forever. Find P if the force of interest is 3%. .H ‘ ,. - . T) (f) , K - f K, ‘ \f as an amwwd i,: Q ~\ : 5©%3%>/va l . V r 0.2»; is; A ‘le/(iﬂ/L 5 :_ a] ‘ M l t. \ C7 r (j C / Li}, 1 \ ‘”‘ Ci. N & lK CK \iﬂ 0‘ ﬂ‘ ’0‘ I“ “: w ”> V '1' S C C, L, \J \,) (A CHE _ l Ck'gﬁ 3 —Qx-.g'§ K \ l ‘“ \ 'a ‘ \| l )JOIUQQ Il N > > : P "—T\> l ‘ <1 l'e ...
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Quiz2Solupdated - ACTSC 231 Fall 2009 1[9 marks A certain...

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