Oct 2005 Term#1 - SIR, Department of Mathematics University...

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Unformatted text preview: SIR, Department of Mathematics University of Toronto WEDNESDAY, November 2, 2005 6:10-8:00 PM MAT 133Y TERM TEST #1 Calculus and Linear Algebra for Commerce Duration: 1 hour 50 minutes Aids Allowed: A non~graphing calculator, with empty memory, to be supplied by student. Instructions: Fill in the information on this page, and make sure your test booklet contains 10 pages. In addition, you should have a multiple—choice answer sheet, on which you should fill in your name, number, tutorial time, tutorial room, and tutor’s name. This test consists of 10 multiple choice questions, and 4 written—answer questions. For the multiple choice questions you can do your rough work in the test booklet, but you must record your answer by circling the appropriate letter on the answer sheet with your pencil. Each correct answer is worth 4 marks; a question left blank, or an incorrect answer, or two answers for the same question is worth 0. For the Written-answer questions, present you solutions in the Space provided. The value of each written—answer question is indicated beside it. ENCLOSE YOUR FINAL ANSWER IN A BOX AND WRITE IT IN INK. TOTAL MARKS: 100 FAMILY NAME: GIVEN NAME: STUDENT NO: SIGNATURE: TUTORIAL TIME and ROOM: REGCODE and TIMECODE: T.A.’S NAME: MQA T0101A T0501D T0101B TOGOIA T0101 C T0601 B T0201 A T0701A T0201B T0701B T02010 T0701C TOZOID T0801A T0301A T0801B T0301B T5101A T0401A T510113 T040113 T5201A T0501A T0501B T0501C FOR MARKER ONLY Multiple Choice - 1 MQB MQC MBA M3B M30 M3D T3A T3B WQA WQB W3A W3B W30 582128 WI 524 UC 52 UC 87 UC 256 LM 123 LM 157 UC 244 UO 328 UC 52 Page 1 of 10 NAME: STUDENT NO: PART A. Multiple Choice 1. [.4 marks] How many years will it take an investment to triple in value at an effective rate of 7%? VI A. 16.5 years 3 1’; (L o 1) B. 21 years C. 42.857 years j m n d3?) 16.238 years n i M E. 1.031 years 1% 6/404} 2. [4 marks] A person owes $1,000 in 3 years and $2,000 in 6 years. If the interest rate is 8% compounded quarterly1 then to pay off both debts in 5 years, he must then pay A. $3,155.03 20 24 61 MW fears 13. $3,469.33 0 .. __ . C. $3,000.00 .000 1000 D. $4,457.84 Lay er] 63) $3,019.35 ‘8‘ Page 2 of 10 NAME: STUDENT NO: 3. [4 marks] A loan of $25,000 is amortized over 10 years at an interest rate of 6% compounded monthly. - If payments are made at the end of each month, then the principal repaid in the first payment fl“: #393 7.2.0129?“ is: A. $277.55 {1 a ::::::: == 30 D. $33.33 R a toofx 23— £00 E. $125.00 g, M {Maggy} #1253 g ’36 2?? 5’? {kg/Li‘qu gm . . ‘ « 3mm” My one. 133-524-er a. d Hind/[fall 0 Al wk 61 e y.) F [74% 2 4 WW?’ ‘ g a W,00{ J ha; {effiij. Z: ( '; 0A 6‘? lfiraygyitf)g‘lf?i5? (X; gyligrg’ £2?11{ (‘éwflj a. ’7 Kr wt 4. [4 marks] A person makes 40 quarterly deposits of $200 into an account earning 4% compounded quarterly. If the first deposit is made right away, then at the end of 10 years, the amount in the account will be closest to: $9375.05 0 3g? 44? B. $9,777.27 “l” .- C. $9,604.89 D. $9,989.08 E. $19,078.05 Page 3 of 10 NAME: STUDENT NO: 5. [4 marks] If a $50,000 mortgage has monthly payments at the end of each month for 5 years and interest is 8% compounded semiannually then the amount of each payment is A. $1,035.63 0.04>1fi0+011 B. $1028.49 2 5’0 @690 —: R Ci - C. $1,057.28 2 E, l '16; D. $1,042.05 6. [4 marks] If a $100 bond has 8 years to maturity, semiannual coupons worth $3 each, and an annual yield of 7%, then its market price is $93.95 B. $90.03 C. $94.65 D. $91.27 E. $92.29 Page 4 of 10 NAME: STUDENT N O: 7. [4 marks] If a $100 bond has 5 years until maturity, an annual yield rate of 8%, and sells for $90, then its semiannual coupon rate is closest to «l0 3.0% jq01|00(|,01fl +100!“ Claw! 2.8% .r m A - ,rts esterth mm“ C 4.0% “Ema” flea. ) {O D 21% 0% I .. GHQ-r [000: E 3.3% lOOr W 0W1”; ( £040.] m»- [00 [:0 5:6? E I Cllflq’) :0] % 9-7’9’?‘ 2.? as G’EO‘fgg-gfl 8. Motor/’63] The system of equations m+2y23 2x+ay=4 has no solution if the constant a is equal to: A. 1 I 2 3 2 0* ‘9‘ R [email protected] ( l 2 3) L > 2 o a"! ’ ii) 01%”) Unlatmev €0LA. as, IQ malmw as {0 ol 9 Page 5 of 10 NAME: STUDENT NO: 9. [.4 marks] C Q a )«l (1 O) 10. [4 marks] The system of equations: 5131 +2333 —- :24 z 1 722 + 2:3 +2m4 : 0 —£Ll _ 333 = 2 —2m —3:t:3 W334 =m3 has A. no solutions B. aunique solution @ a 1 —para.rneter family of infinitely many solutions D. a 2 —parameter family of infinitely many solutions E. a 3—parameter family of infinitely many solutions 2 a a .a- I l O ’2. I O l I Q- o gages {VQg I ‘—————-—? E in o [I 0 9— 0 «2 ’3 ’5 3 i O 2 "I; a Q flQW-tg -l' Raw—9R? __>, (r) | l ‘2 0 q > 3 0 0 5 xi 33 o O “I . a y. Ll Vquch5 #BMM'W" f Page60f10 NAME: STUDENT NO: PART B. Written-Answer Questions 1. [15 marks] On January 1, 2005 a retiree had two ordinary annuities as follows: 1) $3000 payable on January 1st each year, the final payment being on January 1, 2020. ii) $500 payable at the beginning of each month, the final payment being on January 1, 2020. Immediately after receiving the payments on January 1, 2005, he requests that these two annuities be combined into a single annuity, payable on January lst and July lst each year, the final payment being on January 1, 2020. If all the annuities are based on an effective annual rate of 5%, then find: (a) the rate per payment eriod for each of the above three annuities. L) ,m’ or “’7? PW Yew J I a) nos/:0“) 3"” Cgmhoi l'0$y$(i+r)l i Fifi [6] (b) the values of each of the two old annuities on January 1, 2005 (right after the payments were received). jg.“ 1,09 O Page 7 of 10 NAME: STUDENT NO: 2. [18 marks] A $90,000 mortgage has monthly payments for 10 years at the effective monthly rate of 0.4%. [4] (a) Find the amount of each payment. R1 someoxflfl". N, I’fl'ofith—l2@ 63.0, 1,: Raflfiow: 00,000 059?,004 «3‘0 MMWng-W xii? M $43.50 ' (#336? CW 0K 4‘6 . or £93; 9H5:%2 Olaf—67.00% fiézbgflwjt, Mt amm’ge. [8] (a) How many payments need to be made to repay $60,000 of principal? [More precisely, but confusingly, what is the smallest number of payments after which at least $60,000 has been repaidfl Erw‘cifal amt-raging: Mug-{f l/ze, g 155 rel-Maw; TP [A roawa / 30,0630 “3 55"??ng QW.QW m é; TQM ww— 3‘?‘ WVMM f ' Wat/w €00) 55 W fféfl/afl. £1: M..:A<é§ L696 flail .- a. 34 l3 19.41% @l‘wfl) Page 8 of 10 NAME: STUDENT NO: 3. [13 marks] [7] {(1) Find the inverse of the following matrix (if it exists): [6] (6) Find the solution(s) of the following system (if there are any): 2:3 +331 :1 m + y —2z =0 7;) { cc +23; +32 :2 30“,“ i5”. Page 9 0f 10 NAME: STUDENT NO: 4. [14 marks] A person is selling hot dogs, hamburgers and bottles of water. The prices are $1 for a bottle of water, $2 for a. hot dog and $3 for a hamburger. At the end of the day she has made a total of $330. She also knows that she sold a total of 200 items and that the number of bottles of water sold was the same as the numbers of hot dogs and hamburgers sold added together (everybody bought an item of food and a drink). How man hot do 3 did she sell? wig {gt—W Lg’é {Nigel} laa‘igwjij) op lnamlngg/‘fij W614? UV W+3H¢2D 6330 WAW$0H4 M. 1—4 “l 0 93%?“ 9' 4 o l '5 ,2 $390 '5 2 33@ l Riva—£92. C; I L2 (95" $193 c; l 1/7, 95/ 9»?lele 0 C? "' “yo 0 0 l yo r 2 Aaaélc f ’ r T05 W3” agawnggH ,330 l 41.6. I see; w” " C) “if QQ—e Wfi? w A» 3 H «1’7, 0 «a» ((5) 40 T; W / W’rHr/l) / [00 +30%”— ’2 W 0 " “#0 +30 V/ ‘p flay \jfifgfilfllfif mm. l “‘0‘”? eel/Lesa” main (MM 0 A18] vaflaum (540 Cow/Se, skinless, TM a A . MEN-gm; M equflfitams 0rd 104 M D wadlb‘é {(3% M WM Obfhjl :0 er.el;rl€ lg 0 “MC - ~ g2. ,, ’Cl 3% C ‘ mid Valid/0430“) Page 10 of 10 ...
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This note was uploaded on 03/02/2010 for the course MAT Mat133 taught by Professor Igfeild during the Spring '10 term at University of Toronto.

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Oct 2005 Term#1 - SIR, Department of Mathematics University...

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