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Unformatted text preview: 0 You have 50 minutes 0 The following are formulas that you may or may not need; . ,. _ 1
F=(1+i)"PV yn=—L+(yo—J’—)a" F=Qﬂ——R
_ 1 — a 1— a 1
P: 1 F P=(I+')'1R R=———1——F
1‘ (1+ 1)" 1'0 + i)" (1 + i)” ——1
i(l + i)" ,
= +bn R: P 7‘ =1+lm"1
yn yo (l+i)"—l eﬁ' ( )
Bm=(1+i)B,m+R yn=ayn_1+b
Multiple Choice Section:
0 Choose the answer closest to yours and ﬁll in the answers in the space provided on the test form
0 Each question is worth 2 points and no partial credit will be given.
B 1. A person deposits $40 at the end of each month into an annuity earning 4.8% interest compounded
monthly. Initially the account had a zero balance (at the beginning of the ﬁrst month). Suppose we
wish to create a difference equation of the form yn = a y,” + b to represent this situaﬁOn. Letting y.1
denote the balance at the end of the nth month, ﬁnd the values for a and b:
,X a= 1.048, b=—40
@ a= 1.004, b=40
C. a = 1.004, b =—40
/D.’ a= 1.048, b =40
as.“ a=— 1.04s, b.=40
F Math116—Spring2004
TestZAPagel D 2. How much money can you borrow at 9_% interest compounded monthly if you agree to pay $500 at
the end of each month for 25 years? N 305
A. $60,027.67 : .175
B. $56,371.22 3” pu
C. $52 242.54 s no
, M'V
@ $59,580.81 2 u o
E. $51,776.55 E 3. The price of a summer cabin is $70,000. The bank requires a 10% down payment. You take out a
10year loan with 8.4% interest compounded monthly for the remaining balance. .How much are
your monthly payments? N 21‘
33231;? W W 63 M
$795.56 1”“? A.
B.
c.
D $835.34 F v
® $777.74 a 4. The population of a certain country is currently 20 million and is increasing at the rate of 1.5% a
year due to births exceeding deaths. But, the population is also decreasing by 100,000 people a year
"*dueJo emigration. Let yll be the population (in millions) aﬁer n years. The difference equation satisﬁed by y“ is:
”% A” yn = 0.1 + 20(0.985)“
B. yn = l.015y.,.1+ 0.1, yo = 20 6 yn= 1.015y,H —0.l,yo=2.0
pr yn=0.985yn_1—0.1,yo=20
,2.’ yn=0.985y.,.1+0.1,yo=20 A 5. For the difference equation y" =’—— 0.3yn.1 + 10.4 , which of the following initial values will make
the graph of the difference equation a constant graph? i® Yo = 8
B. Yo = 0
C. Yo = 0.125
D. yo =~ (102/3)
E. Yo = 10.4 B 6. Calculate the effective rate of interest for 7% interest compounded biweekly (once every 2 weeks)? A. 7.62% 1 5 5 25”
7.24% — ”“5
C. 7.12% b
D. 7.51%
E. 7.19%
? Math 116— Spring 2004
Test2APage2 D 7. You have decided to buy a new stereo for $2500 and agreed to pay in 30 equal quarterly payments
at 1.25% interest per quarter on the unpaid balance. How much are your quarterly payments? , N 3 0 “715 Yﬁarzs
A. $101.42 ”r ,5 n;
@100.“ JV ' S o
c. $97.8 ( 2 0
was/777% Wt
E. $69.20
F U o For guestiong 8 and 9, consider the following diﬁ‘erence equation (in dollars) and initial value:
y1‘ = 1.0537,” + 200 , Yo = 500 B 8. Describe the longrun behavior of the graph of the difference equation [\A an 6
A. Constant
@ Monotonic and Repelled F: p e H (A
C. Oscillating and Attracted
D Oscillating and Repelled 2 ()3
E Monotonic and Attracted \“ \. o 5
J4 0 O o
D 9. Find the value of 3’12 . Round to the nearest dollar.
re: A. $898 X” lacCHM 1% Zoo
33 B. $3,298
é C $2,900
I 63 34,081
E. — $2,285 C 10. How much money should be deposited today in an account that cams 10% compounded quarterly
so that it will accumulate to $3800 in 10 years? A $10 203 24 ‘ "U ‘1 D
a . , . . \
B. $2,384.76 .2 q i Z 3
@ $1,415.24 1 ‘ o
D. $1,465.06 WW
E. $3,651.07 F a 5 300 [5: 11. Alexander is setting up a retirement account. If the interest rate is 5% compounded annually, how
much will the account be worth aﬁer 45 years if $2200 is added each year? A/ HS
@ $351,340 » 1; s
B. $100,097 79‘) Q
(2. $325,872 PM “,0
D. $19,767 .3 W
E $110,713 1 Mathllé—Spn'ng2004
TestZAPageB E 12. When making a rough sketch of the difference equation yn == O.6y,,_1 + 20 , yo = 10, the dashed line
that is drawn is‘which of the following lines? A. y=20 ??0
B. y= 10 ‘9
c. y=1zs \— 0 b
y = 1.6
y = 50
Short Answer Section: 0 Show your work on this sheet and mark/identify your ﬁnal answer clearly. 0 Partial credit will be assigned for the appropriate work. Full credit will be given when your work is
shown. 1. On December 3 l, 1995, a house is purchased with the buyer taking out a 30year, $200,000 mortgage at
6% interest compounded monthly. The mortgage payments are made at the end of the month.
Calculate the following values. Round to the nearest cent. . N 356
A. (1 Pomt) The monthly mortgage payment?  I ,5
$ “015th W ‘?oo,ooe
7.9M“l
PU O B. (1 Point) The total interest paid on the loan? 33 23\ I676 ,33 C. (1 Point) The interestpaid during the year 1996 (year 1)?
~53 m 6133 . m D. (1 Point) The balance of the mortgage as of December 31, 2010 ('15 years into the loan)? §WHZ,UQ7,69 Math 116— Spring 2004
Test2APage4 2. Consider the diﬁ‘erence equation yn = 0.5V...) — 4 , yo = 1000 A. (1 Point) Generate yl , y; , y3 using the difference equation. Show how you arrived at your
values. VO 1 ’O;§(’OUO) r"I )4 '; VQé
>41 05C‘46/63~ ya; 2,4,,
VI? O~SC'?W1\‘4 r )3: “‘3 B. (1 Point) Solve the difference equation. Simplify the solution. .31 ‘ 8 VA Ligtgmr %\\ (c3535 I —.5 \;"’:_3?K = .e +€lwel (0,5)“ I C. (1 Point) Use the solution in part B to obtain y; . Show how you arrived at your value for ya . ya = ‘8 +619083CO.3\3
yen —"lt 062$ D. (1 Point) What is the vertical direction behavior of graph of the difference equation: Constant,
Monotonic, or Oscillating? Explain how you arrived at the answer based on the value ofa.
M0“) Its (ﬂows JR: ht Mghakwlg 6164““ U41»:
Alkmt' A "' VPUSWWL 6" the N} (0% 3‘1”“? 6““‘4‘ .'..% 0(on pﬂ 'C‘1K0L\ 1000
i E. (1 Point) What is the long—run behavior of the graph of the difference equation: Attracted,
Constant, or Repelled? Explain how you arrived at the answer based on the value of a. TIT—ls amtb i’0 {36 Ck‘lr‘l'QCFfp‘ 6rcuw< 0.5 4. I
4kal~ "\Gan if: Rikr‘a (ling . Math “6—8ng 2004
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 Fall '05
 HERNANDEZ
 Math

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