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Unformatted text preview: MATABl Tegtl Sonnets. Od— lo, 2.00% Part A — Multiple Choice For each of the following carefully circle the letter next to
the answer you think is most correct. Each correct answer earns 4 points and no answer/ incorrect
answers earn 0 points. Justiﬁcation is neither required nor rewarded, but a small workspace is
provided for your calculations. 1. To the nearest cent, the present value of $ 60 due in three years at 3.6 % APR compounding
quarterly is (a) e 89.25 (b) $ 57.88 (c) 8 58.41 $ 53.88 7 ~47...
Pv: co (1.0m) a: 53.88
(tgj—(D
4 2 100°!) 2. To three decimals, What interest rate compounded continuously is equivalent to 5.1 % APR
compounded every three months? (a) 5.057 % (b) 6.743 % @5068 % (d) 3.801 %
o o S l 21 4 a: elements) 2 Soﬁa/o 3. The future value of an annuity due is $ 50 and it consists of 5 payments at 6 % APR com—
pounding monthly. The monthly payment to the nearest cent is (a) $ 9.23 (b) $ 8.19 @$ 9.85 (d) none of (a), (b) or (c).
5
Long) l
So:—R ( (was) re
.00 5  R x 01. 8 5
4. If = m then the value of Mr) is
(a) 4/5 (b) —4/5 @—1/5 (d) none of (a), (b), or (c) lows—(VAM—S) «a; Jliwx l'l[¥);/Qle\ 1’5
(3(“400'5'?” X'J’dl {*4 1+] 5. The least number of months it takes a principal of S P to increase by 40 % at 4.2 % APR
compounding semi—annually is 102 (b) 97' (c) 96 (d) none of (a), (b) or (c) 21‘: ‘ '
I.4%=~?(l:020 i 'l’r» tel: Hears « Compoumolrnﬁ
is sewn AMNVALD/j t2: Mala} it; <3,OG[5 we (Dental 40 aftMel— 2/9’“(l‘09~)) HléHE$Tém0k+kS
‘2: Q'S‘AQMS 4» 102mow+k$. 6. A bank account gives 5.2 % APR compounding weekly. Assuming the account starts empty,
the least full dollar amount your parents must deposit in the account now so that you can
make a withdrawl of $50 at the end of each week for the next 52 weeks in a year is (a) $ 2,668 (b) 3 2,600 (o) $ 2,485 $ 2, 533 “52
[~— (1.009 r00, pV: 50 ’2: 2,532'53 3
7. The limit 11m ( 2m —x)
woo :2: "~53: (a) equals 0 (b) equals 00 @ equals 5 (d) does not exist 3 2m
_____Z(_.~—~ H‘Ik .3; X/KFXS/{ISX "’1’ S 0L3 XrE'CD
x‘msx xii—5;: 8. Given an effective rate re the APR 7"% compounded every other month that is equivalent to
are is (a)r:6(m+1) (b)r=m @r=6(€/§+—u—1) (d)r=67‘e—~5
(a
l+ll350+§) Solvergr JL'. H g— ,» mMWU Part B — Full Solution Problem Solving 1. A debt of $ 8, 000 due 4 years from now and S 4, 000 due 8 years from now is to be repaid by
three payments: (1) the ﬁrst payment is at the end of 2 years from now;
(2) the second payment (which is 3 / 4 of the ﬁrst) is made at the end of 38 months from now; (3) the third payment (which is 2/3 of the second) is made at the end of 7' 5 months from now. If interest is 4.8 C70 APR compounding monthly, calcukate the value of each payment. (Round your ﬁnal answers up to the nearest dollar. A moneytime diagram is required for full
[12. points]
3!— LJLJT K: amorawh 0? 1 PGUQMW+ in 4 33090
MonE‘jwjﬁme inﬁrm Ts (291$th 41 0 tau/WK O > " POL?“ D4 '1 1‘5 h" wow‘hhs
14 5% 4s ' 12.25: on, points). ‘ i 1 1’ 2
9 g z 2
3 I i g
i
s i
E!
s a . '04s
iqdmhw 0‘? VQUE ‘ (A: T; c: .004) 2. (a) Imagine winning a very large iottery. There are two banks in which to consider investing
your winnings: Bank A pays 5.54 % APR compounding monthly and Bank B pays
5.52% APR compounding daily (365 days = 1 year). Which bank is the better choice
to invest your lottery Winnings and Why? l , [Spoints]
Tke “View choice” is ‘We \Oomt w‘rHA ‘Hie
weaker eHjeci‘we. mkz.
0554 '2
We) =—(l+ ' )«p—Lx weeszﬁ'sa—z
fl \2
365
(A€)B: + '05“) 41 iowaéﬁtsss
3625 e \\
(P)qu A \5 If bccmﬁee (as Seen in “Hm 4% ci‘pl (b) Assume now there is a third bank to consider (Bank C) which offers 7‘ % compounded
quarterly. What value of 1*" makes Bank A and Bank C equaliy attractive for the invest
ment of your iotterywinnings? Round your ﬁnal answer to three decimals. golve ﬁwr‘ where
a aux—e “EV
reﬁt? 'ofiqlgala 2:: .0ssesoi5} [6 points] 3. Find the annual continuously compounding interest rate that would cause a principal to
increase by exactly 132% at the end of 4, 234 days (365 days 2 1 year). Exprss your answer as a percentage rounded to two decimais. [6 points] 6—2323“ I; H: égwurs Eur/(ease, \otj [3279
5605 $0 “Pa 232?
Pr, T7rtnotjo0k}  «94232) A» amps/43% rah1.2570 4. Find the value(s) of the constant c so that 112% f(:1:) exists Where
mm; 363‘s if $<2 m $~2
ﬂﬂ { 62272 if x > 2
Justify your solution completeiy. [8 points] “ 1&2 and We dePnH‘fovx 0'? ﬂ changes I glunchgng 0):)” 2) we, evatumk 1" Stoleoi limit/Hg in“ 19”); QRM'C‘” ) ..,., ﬁrm 6gz+2><+40 X41” 5. For each of the following, evaiuate the limit or state why it does not exist. 1w m—Z
[8 points] (a) 31311; 93mg :M(\”m' \44'3"; ) ¥”5 *‘5 1+ (hp—2. WW VW'ég (W5) 0+ W) ,5 M 4323;“
xr—a 3 (X—3)( \+ (ht—2 ) ., M #:ﬂiw.
x’ég ' H 1—2. (b) mars: + :3, [El [5 points] ’ V5440 (0th {NM Xxob W x—d—O 30 We eye/Jr [a abovﬂ. 6. A bank account pays interest at 6% APR compounding quarteriy: On your IT—th birthday
you deposit 3 1, 000 into the empty account. Beginning with the ﬁrst quarter after your 20‘th
birthday, you make a $ 750 deposit into the account at the end of each quarter up to and
inciuding your doth birthday. Then starting with the ﬁrst quarter after your 40—th birthday,
you deposit at the end of each quarter $ 1,500 up to and including your 62—nd birthday.
There are no further deposits after your 62nd. Catcuiate how much you will have in the bank
account on your 67—th birthday. Round your ﬁnal answer up to the nearest doliar. [12 points] @9 FIWC‘L\ OLWGUVKJK' =_ A; 4: A2, ~t A3 org (anouus. 200 F)" (5014:: 29009;”!(«53 é?
5106;061:015) .__._.__.__——————————“" c 80
z. 7250 @2241 (1:06)“) ‘23 #015 ...
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This note was uploaded on 06/11/2011 for the course MATHEMATIC a32 taught by Professor Grinnell during the Spring '11 term at University of Toronto Toronto.
 Spring '11
 Grinnell

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