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Unformatted text preview: Solve/i Department of Mathematics
University of Toronto WEDNESDAY, October 31, 2007 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 multiplechoice 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 writtenanswer 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 your solutions in the space provided. rI‘he 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 D m
T0101A 881084 T0501D W3
T010113 881086 T0601A BAA
T0101C 881087 T060113 RAB
T0201A 882108 T0701A FEA
T020113 , T070113 F213
TOZUlC T0701C F20
T020113 T0801A FSA FOR MARKER ONLY
Multiple Choice T0301A T0801B F313 T0301B T5101A MBA
T0401A 881084 T5101B M5B I
T0401B 331073 T5201A MESA
T0501A 881086
T0501B 881083
T05010 882106 TOTAL Page 1 of 10 NAME: STUDENT NO: __
PART A. Multiple Choice 1. [4 marks]
What nominal annual rate compounded weekly is most nearly equivalent to 5% per year
compounded quarterly? [For this question, 1 year=52 weeks.] A. 4.89% r" 1 mammal ammwal ma, 1?...
B. 4.97% L w + :ww. . 09% I I)”,
115.00% r/ G+hgj)‘:l E. 4.93%  57 ‘l 2. [4 marks]
A loan of $10,000 is to be repaid with payments of 33 X one year from now and $2X three
years from now. If the eﬁective annual rate of the loan is 10%j then X = 4146.42 0 .1 3
M B. 3908.54 10,000 X 2X 3
«:3. 3769.47 ( ‘OYuZKCI m)
D. 4561.06 IOJOOO ’ X I.
E. 5017.17 X j W; C1.to)"+ 20.10) ’ Page 2 of 10 NAME: STUDENT NO: __ 3. [4 marks]
If interest is compounded continuously, what annual rate (to the nearest 0.01%) is required
if the amount in an account is to double in 8 years? A. 12.50% ' P t: P er‘ﬁ
0
B. 7.92% 91"
o. 9.05% 7 Q 0 i ﬁve
10. 10.63% at
1 '3: Car
is. 3.66% 4. [.4 marks]
A father deposits $1,500 in an account on the day of his son’s birth and continuesto make
similar deposits every year on his son’s birthday up to and including his 17th birthday. If
the account earns an effective annual rate of 5% then howmuch will there be in the account on his 17th birthday just after that day’s deposit? l5" ll” ' ‘7 Malia» ’* At $40,698.58 a
,CIWLW awareWm
13. $17,534.36 1500 $600 $00 {cg Waymiﬁ. $42,198.53 ‘
D. $38,760.55 E. $37,260.55 06W WY") “9:7‘ 31
15000.05)‘ + W00 “'" T4105” 90c «a6, 3am e
(ﬁt/Lg can Page 3 of 10 NAME: STUDENT NO: __ 5. [4 marks]
How many semiannual interest payments are remaining for a $100 bond with annual coupon
rate of 4% and annual yield rate very close to 4.5% if the bond is selling for $96 per $100 of
face value and the next interest payment is in 6 months? A. 18 . 9n 20 org 1 [w 4" 2a ‘37 ADng +5
to. 10 Cid, ‘3 100 0.022?) '9’ D. 15 " Om";
E. 24 _ 6olva par Galas/T ' M 0 6. [4 marks]
To purchase a $450,000 house a pers0n pays $50,000 down and takes on a 25 year mort—
gage with monthly payments and interest at 6% compounded semi—annually. The monthly
mortgage payments will be closest to: A. $2,899 Lf {0’ {O} '5" R a 7300 “i
13. $2,167 l7, 2. (3. $2,577 Q —r a i 03) (D $2559  R4. W 11; $2,599 ‘ ___ (H, ,L) 000 03) E11— 1 M9 1__g,o:s Page 4 of 10 NAME: STUDENT NO: _ 7. marks] A 20 year loan for $100,000 is to be amortized by equal semi—annual payments. If interest
is at the nominal rate of 10% per year compounded semi~annua11y, then the semiannual
payments are $5,827 .82 (You can check this if you have time to waste.) The interest in the 21st payment is closest to R O ‘ @1299 (2Q an F07 wgﬂ‘ﬁ [5‘ A. $2,914 g I Eygmao
(119mm 532?.‘32 ] (1 ’) j
C. $3,847 8 06 mam/£5
D $3,914 Vac/Mia “ape/e, We "2,0 fay
E $4347 \FMGILMLM  L
“Irv? axe/Sf if . we’l‘v Fﬂymdwf
‘ o
‘3 ,0426 9. . {ﬂy/o]
1. 5872‘? 37$ 1 «6 06
“: stSIaa. 8 [4 marks] 1 2 0 2 1
Let A_(0 1 3) B—(_1 1) o_(1 3 4) Which (one) of the following products exists? A. 0—13 ' a. c” («a/Wt “(Sf { l A.
B. CTAB B as: “) await WWJ'T]
((933724 J (
M
D. Als 1 at 3 ‘ 5!
E. BOB—1 C. lEja‘B (LA ails5 D. P‘ “w L,
1 3 MM ‘6 9,2
E. 1% ‘C’ C/W/Wlptfarlteﬁﬁ Page 5 of 10 NAME: STUDENT N0: __
9. [4 marks]
The system of equations
as —— y +22 3 1
at —52: m—l
3:3 +211; — z = 2 has A. the complete solution a: = W1, y z 2, z = 0 B. the complete solution a: = 5z — 1, y = 2 — 72, z any real number
C. the complete solution x = 4, y = —5, z = 1 . the complete solution :1: = (3 — 5y)/7, y any real number, z = (2 w y)/7 D
3 ' ’\ no solution \ I Q g‘ 10. [4 marks] 1 0 1
The £1.32 entry in the inverse of the matrix [1 l 0] is
0 2 1 A. 1 o
> I l0
@ "‘2 .. 9~ (9 l l 0/0 [213 girl" 13*?” ,5 )0
C. 0 i .l 0 C? l 0 7 1' @05 —21 0 9A g o 0 l O
Q «*7 421' l O l l 0 o
_.1_'..———" O l I l "I! O
_.. , __ l
Q3 793483») o O "l 1 9‘ “A
gal/Wt “(gwa 1: ’2
Q ,9 >93 W‘g‘w I 037.
,L———? O O ‘ 2 , "L Page 6 of 10 NAME: STUDENT NO: m
PART B. WrittenwAnswer Questions 1. [15 marks]
A pile of coiris consists of nickels, dimes, and quarters. There are 18 coins in the pile. The
total value is $2.55. The number of quarters is one more than the number of nickels.
How many nickels, dimes, and quarters are in the pile?
[For full marks, make sure you use rowreduction to solve the system of equa— tions.] L643 ﬁr midweek
6L 7, iii ﬁfthws A. 7:, 3'  N+o¢ﬂ ﬂ‘g N ngs~§z
5N +IOD+15&.: 255’ I‘MD "‘ "
eewﬂ D
‘3'
‘3‘ 5 i I 17” if %wo 6’1 bedkm? S Al‘éxﬂmﬁﬁHJ aubs‘tttw‘éc @r’ My“ M 7N4”) :1”?
N+DTNH €43 302N4,{0D~:280
{N 4400 +7.5CU*‘)‘75{
1N+DclﬁL (1 3N+D 7’23 a _l
\4 El) Ni W“ ‘ 1 W)
BgkQ/S‘Bl” 8:3“? 19 ( I 3 13> (O (I ’(o
D M ‘ a
/‘ 7‘ ‘17 40 Nﬁg’ Dipiqﬂlliro
“WQKO ' @ a4&9N*'“4
‘ a game xMQW 60a.
(9J— J 0 l (I Page'ToflO NAME: STUDENT NO: _ 2. [16 marks]
The input/output matrix for the industries A and B is given by: Industry Industry Final
A B Demand
Industry A 100 300 E 100
Industry B 300 225 E 225
Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Production 100 225 w
Factors If the ﬁnal demand changes to 160 for Industry A and to 200 for Industry B then ﬁnd:
[12] The new total outputs for the industries A and B. “179.84% gibbon? A 1500 Tate! 0.439wa B 1150 r o... 3.1.. 2. '3 /
Tad" MAW“ " 5’“ 5” Lawn *’
. 9 "6 3i. ’3;
s TE 5
i' " .2. r Page 8 of 10 NAME:  STUDENT NO: __ 3. [14 marks] Veronica has won a lottery which will pay her $3,000 each month for 1 year, and then $1,000
each month for the next 3 years. She will receive her ﬁrst $1,000 payment 1 month after
her last $3,000 payment. If she invests each lottery cheque just after receiving it, at 4.5%
compounded monthly, what will be the amount of her investment immediately after she deposits her last lottery payment? Page 9 of 10 NAME: _ STUDENT NO: __ 4. [15 marks] A bond with an 8% annual coupon rate and semiannual coupons has 25 coupons remaining
with the ﬁrst one cashable 6 months from now. [10] (a) If the bond is currently selling at $120 per $100 of face value, ﬁnd the annual yield to
maturity. [The price should be correct to within $1 of the actual price per $100 of face {4,09 value] #26,”
_20:{00(l4.4) 4H Qﬁmi‘ P7100 1" '03 “:9 P7 llﬂiql £90 low 9‘ Vidal .4730 ,n 11,026 5v Pg gamer any; as
4 ’ .026: ea. P == H23 M [5] (b) On the same day as in part (a), the issuers of the bond announce that those‘who so
choose will be able, in 5 years time right after the coupon payment, to exchange each
$100 of face value with its remaining coupons for $105 in cash. If the annual yield to
maturityremains the same as in (a), what happens to the price of the bond? [Numerical calculation, with explana "on please] ‘0
l ‘ ' f, m w am!
(We, [59% MC awﬂ't [IA Odgl/I 5 If cm W a men . F H greatest, Page 10 of 10 ...
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