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Unformatted text preview: SIR, Department of Mathematics
University of Toronto WEDNESDAY, November 2, 2005 6:108:00 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 Writtenanswer 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. 133524er 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% jq0100(,01ﬂ +100!“ Claw!
2.8% .r m A
 ,rts esterth mm“
C 4.0% “Ema” ﬂea. ) {O
D 21% 0% I
.. GHQr [000:
E 3.3% lOOr W
0W1”;
( £040.]
m» [00 [:0
5:6? E I Cllﬂq’) :0]
% 97’9’?‘
2.? as G’EO‘fgggﬂ
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 ﬂQWtg
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. WrittenAnswer 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
MMWngW 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 amtraging: Mug{f l/ze, g 155 relMaw;
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 . MENgm; 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.
 Spring '10
 igfeild

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