t1s1_20081010 - MATABl Tegtl Sonnets. Od— lo, 2.00% Part...

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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 4-0 aft-Mel— 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 Xr-E'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+§) Solver-gr JL'. H g— ,» mMW-U 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 money-time diagram is required for full [12. points] 3-!— LJLJT K: amorawh 0-? 1 PGUQMW+ in 4 33090 Mon-E‘jwjfim-e 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 e-Hjeci-‘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 2-32? Pr, T7rtnotjo0k} - «94232) A» amps/43% rah-1.2570 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' \4-4'3"; ) ¥-”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 do-th 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 62-nd. 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.

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t1s1_20081010 - MATABl Tegtl Sonnets. Od— lo, 2.00% Part...

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