Math 70 - Test #2A - Spring 09
Row_ _ Name
8.5, Chapter 3
Score:
50} ~-k~.
A <?c..
80
Where appropriate, and whether or not you are using the MATH SOLVER, you must
•
Name the formula
•
List the values that are inserted into each ofthe formula's variables
•
Box the variable that you solved for
•
Place your labeled answer in the box to the right. Monetary values should be rounded to the nearest
penny. Other decimal answers should be rounded to four significant digits to the right of the decimal
point.
•
Q1:
If you are not using the MATH SOLVER, you may use scratch paper to do your calculations.
Expected Value: A card is drawn from a standard 52-card deck. If the card is an Ace, you win $10;
otherwise, you lose $1. Set up the payoff table and find the expected value of the game.
/0
~I
Pi
Q2: What is the annual percentage yield for money invested at
A. Formula
A. 9.3% compounded semiannually? . 0 q S I (P
B. 9% compounded continuously?
• 6 q c.; I :;
C. Which is the better investment?
It
ttY"
9,3'2 tmpJ
~~~.
fl pq
.,.
Ans: • ()
1 {):J..
B. Formula:
Ans:
0.
nt-
.
.:
9·5'2 ?o
t! I-t f
't
D1 ~~ "'" 9. 42-~
..fv.,-c-C-.
q
,+
4 &> ~ q. :rs- ~ \~
Q3: At what annually compounded rate must money be invested,
t!.-,=-,-I
__
Formula __
if it is to double in 5 years?
t:.I
A ::=
.E :::
~
~
I
20C
I
()O _
):£ '" R. ~~.-=-'
/11-':5
Q4:
Ans:
1."00
~
_ _
_
J
ek..·
lODe>
~~
Rental costs for office space have been going up at 4.8% per year compounded annually for the past 5 years.
If office space is now $35 per square foot, what were the rental rates 5 years ago?
A -= 3 S'
L~p_-::_o?_r_.\_/·_=1
I : : .() tf8
N
-.;1
5
Formula __
(l_(
__
Ans:
l';{ 1'.
Page 2A of 3
Q5:
-"') ~ar+er-~ ~
If $2,000 is deposited each quarter into an ordinary annuity paying 8% compounded quarterly,
A. Complete the balance sheet for the first three quarters.
period
deposit
interest
balance
1
2,000.00
0.00
2,000.00
• 0 l. (Zt:JDO )
2
~/O/)O
J. ~() '0
2. (<;, () 4~)
¥'o.
I
.07.
J.t 0 "'0. 00
Jfo
• £)
3
vO
~,/7..()·go
~
B. When will the account have a value of $100,000?
[F;;:
Formula
"ool
/0 6 ,
= .2.00 0
I = . £'$'/ <4
Ans: ,'Is ~a.-t.-~ •
,5
;v':: 35
t)
FV'
8·::"s ~.
"::!-
0"2
•
03
Q6: The Hartford offered an annuity that pays 4.8% compounded monthly. What equal monthly deposit should be
made into this annuity in order to have $50,000 in 10 years?
Formula
F
-.: : S- tJ,
ts
=
.:c
(;" 0
.3~5. '-I~3
~
N ::'
Ans:
_ _ _I
F V
:'.3 ~ s: t-J 6"
J
.04gIJ'l/O¥-J2:::: I'"UJ
Q7: A stock trading company charges a commission of $20 + 1% ofthe principal for both the purchase and sale of
stocks. An investor purchases 200 shares at $21.50 a share, holds the shares for 26 weeks, and then sells the
stock for $25.00 a share. Find the annual rate of interest earned with this investment.
J:)
-,
~l
cJ.oO (2 I.SO)
~3(/o
~.3
+ (:lD
+
t· Ci J (43 tJo)
5.1.'
)
Formula:
t,3
(p -3
tloo (:lS) SOD 0
----
~9.3o
Ans:
(~{)
=ro
A =-1/0:!>D
pr;; J../3bJ
[R:=, .25'1'1' ]
I
-:: .S"
.2 Co C7Zo
53
10
Page 3A of 3
Q8: A retiree has an annuity that pays 5.6% compounded quarterly with a current balance of $30/000. He wants to
make equal quarterly withdrawals so that at the end of 5 years the account balance is $0.
A. What is the value of each withdrawal?
r------------,
B. How much interest was earned during the first year?
Formula
fl.
p V =-
B. 0--6~
3D,DDO
[f=
R
==
lT3 0
. () ~/'-f
== .01
'r
l! aJ.vL. 1; &
'l
f\J=J£c,
A. Ans:
$ ) T 3D
B. Ans: $
I b b f .9 3
PV -=- Jt.1, to tf~·/3.
lVvtd
·iiJ
P \('
.;lO
~
kJQA~b-tr
2:;0,000 -
::;
;l</fe,</(?/~
:fi'53
SI·S'=!
I
r3vd:: k~
~'30. za )( Lj
:'.~+~~
= &;
q,;",o.'[jo
~ 9 ~o . &0 - 6" 3 s; J, f'-7
I !5"7P 8. q. ?>
Q9: A family has a $150/000/20 - year mortgage at 6% compounded monthly.
A.
Complete the amortization table for the first two payments.
Period
Payment
• 065' (WI1pd.
0
reduction on
unpaid balance
interest
0
bAa)
unpaid balance
wn1'c:l baQ
prnt-lM~
0
0
recl.tu..
150/000
i
J5,,/{)PO
1
1074.65
(,f)O~)
3!J.1. lP5"
f.-5tJ
1 qq, ~ ~S·3S'(.()tJn J b 'Y-'f. (,5 - -=l</f'. :'0
1074.65
2
'1-t/R.
J S-O, ()oO -
/D14. {p5 - =7-{;)[j
/L/9 q, rS. Sf>
I
jqq,(''l-s.?><f:- '32l,.H
3.:2-(,. ~ '::j
3D
32-'/." r
ILfq 3'FJ.tJf
B. After 5 full years of payments, what is the unpaid balance of the mortgage?
C. How much interest is paid during the 20 years?
IS .
[p V:::
s
L
N
.=:;
~
;::
I 'J.
1;?J Lfq. 2> q 8'
]
)61-4. (, ~
Formula: __
P_V__
-=$(;l5~/9J&
.ooS-
f/YI~h
c2L/o-5{f~) :::/8"lJ
~
#p~~
~. h/a.Q. ~=
=10 H·bS:( ()jfo)
Lef':.
to-/aJ2pL -
B. Ans: $/.:lT,3'1q. Lj()
tt>o,ootJ
::: /61-, If 1&
C. Ans: $/IJ 1-, q I
{P
Math 70 - Test #2B - Spring 09
Row
8.5, Chapter 3
Name
Score:
50 i u.. --h ~ E ~ b
80
Where appropriate, and whether or not you are using the MATH SOLVER, you must
•
Name the formula
•
List the values that are inserted into each of the formula's variables
•
Box the variable that you solved for
•
Place your labeled answer in the box to the right. Monetary values should be rounded to the nearest
penny. Other decimal answers should be rounded to four significant digits to the right of the decimal
point.
•
Q1:
If you are not using the MATH SOLVER, you may use scratch paper to do your calculations.
Expected Value: A card is drawn from a standard 52-card deck. Ifthe card is an heart, you win $5;
otherwise, you lose $1. Set up the payoff table and find the expected value of the game to you.
.5"
Pi
-52I?> -- .,.
3'1
~
5:1.
I
Q2:
I_E(X)_=
l'
3
=~
What is the annual percentage yield for money invested at
A. Formula
A. 8% compounded continuously?
B. 8.1% compounded semiannually?
.D8Z.lo 4
{£=
R. ::::
Ans:
8 l:7o
C. Which is the better investment?
AP'1
_I 6J
._=>O
-J
Xi
L~ ::.
J
.0 9 J
P.
~
Crm
p.
oS 32 8'
cer.,+.
]
C 11 P'1
• () S' 33
A P ~
B. Formula:
Ans:
.0
-=- 8.3~'"
8 2. I.JJ :::
8.:J.~ %
,0'6
M-:::-7...
Q3:
At what annually compounded rate must money be invested,
if it is to double in 6 years?
A ::: Z.
p::)
or
oR
rr
z..oo
~
Formula
(!. I
Ans:..
,
2000
e+c.
OR
"'
1%
1000
ItJD
J
Q4:
Rental costs for office space have been going up at 3.8% per year compounded annually for the past 5 years.
If office space is now $25 per square foot, what were the rental rates 5 years ago?
I
r-p
f<.
.=-~.;.
~
.f)
T?S
-
38
!J
Formula
ex_
Ans: $c::2o
.o_~_
Page 28 of 3
Q5: A stock trading company charges a commission of $20 + 1% ofthe principal for both the purchase and sale of
stocks. An investor purchases 200 shares at $18.50 a share, holds the shares for 26 weeks, and then sells the
stock for $22.00 a share. Find the annual rate of interest earned with this investment.
CI fj . S-0)
d. DO
3
t-o}7lrn i S sin"! .
of
:; 99-s-q
.
_
Ans: • 3 0 82:= 30,
8 aza
.:lO
C
-
.
(!Arr~~
c2QO ( :2:2.) ~J.ftJD
Formula: _S_J
I- (2. 0 +.41 ('3.:}- (0)
"1-00
+
.
IT
01 (4'-100))
P
1/ 3 3{P
[~
1
~ 433(P
3:}- s-:r
:='
.:: • B0
~
8
~
]
. b
Q6: If $4,000 is deposited each quarter into an ordinary annuity paying 8% compounded quarte~ly,
A. Complete the balance sheet for the first three quarters.
.::';l .;z G1D f~ ~a,..r+e-r
period
deposit
interest
balance
1
4,000.00
0.00
4,000.00
2
#.POlJ
,
3
1,00 ()
,0 ~ (tf(JlJ())
~O
• C>"). ( 'do 80)
1(P1.
(p~
Formula
FV
8'iO~·OD
/.!Ji t1JjJ. {PO
B. When will the account have a value of $100,OOO?
F =
If) oJ
,
.5 ::::
.I=
~e;D
()
.08/4
::::.02
Jrf;=
~---
------I
~
Q1: The Hartford offered an annuity that pays 5.5% compounded semiannually. What equal semi-annual deposit
should be made into this annuity in order to have $80,000 in 10 years?
F V :::: fD ,rrt;v
[ 5
= 305"3
Formula
.~
1 -:;. . 055/~
=>
Ans:
/D *'';<'
'P..E 05 ,3. 9-'1
.o~ 75
tl
N ::::-
FV
:::- 8-D
~ m trYI+/..
$'.:( 01". iff?
to
Page 3B of 3
Q8:
A retiree has an annuity that pays 5.2% compounded quarterly with a current balance of $30,000. He wants to
make equal quarterly withdrawals so that at the end of 5 years the account balance is $0.
A. What is the value of each withdrawal?
B. How much interest was earned during the first year?
_
Formula -'PC-....LV
® PV=
s-=
\
R :::
$.
30 I OoD
1=i-/"3·J2
. () 5
;;J. /4
J
A. Ans:
1-:;-/3. ;;J...
B. Ans:
~ /'-I5S. q 2.
-= • CJ I '3
tlM&.. py:; Q1 1 ~f)3.t.jt.j
~ (3CJ,fTO O - t;t4-, bD3. '-1-4) =
Q9:
53~t.e.50.
A family has a '$200,066,20 - year mortgage at 6% compounded monthly.
A.
Complete the amortization table for the first two payments.
B.
reduction on
unpaid balance
interest
unpaid balance
• OD t' ¥ £¥)PJ btJ pmt ~ mfe.+-e.st /.\.npJ bal - rcJuaJ,j.....
Period
Payment
0
0
1
1432.86
/tJt;"
2
1432.86
q q;;.. 811
0
0
200,000
L/3.2.~
/11, !Jb9. J ¥
'/35. 02..
/q9,/32./Z
After 5 full years of payments, what is the unpaid Qalance of the mortgage?
C. How much interest is paid during the 20 years?
C.
e.
J
P ;: /fpfj,
119.
f;
B. Ans:
S =
(..;
/J' •
;432. ~b2.
T .:::
.005
/'I
~1tJ -5(1'4 =J~f~t.s
=:
fJ ~ -
PV
Formula:
")..0 ]
~t
200"
(){)l)
_-~
I 7L13 2
. cg' Cp
/
*
';}"I{)
L/3/~~,'-Io
;::
.3
-
JJ.j 31 off b . '11)
-,:; (') 0, tJ(j ()
- z..oo,tJolJ
It. 1" ?-'1Cf·
:J-o
Math 70 - Test #2A – Spring 09
8.5, Chapter 3
Score: _____
Row_____ Name__________________________________
80
Where appropriate, and whether or not you are using the MATH SOLVER, you must
 Name the formula
 List the values that are inserted into each of the formula's variables
 Box the variable that you solved for
 Place your labeled answer in the box to the right. Monetary values should be rounded to the nearest
penny. Other decimal answers should be rounded to three significant digits to the right of the decimal.
 If you are not using the MATH SOLVER, you may use scratch paper to do your calculations.
Q1: Expected Value: A card is drawn from a standard 52-card deck. If the card is an Ace, you win $10;
otherwise, you lose $1. Set up the payoff table and find the expected value of the game.
𝑥𝑖
𝐸(𝑋) =____________
6
𝑝𝑖
Q2: What is the annual percentage yield for money invested at
A. Formula __________
A. 9.3% compounded semiannually?
B. 9% compounded continuously?
Ans: ________________
C. Which is the better investment? ______
B. Formula:__________
8
Ans:________________
Q3: At what annually compounded rate must money be invested ,
if it is to double in 5 years ?
Formula __________
Ans: _____________
6
Q4: Rental costs for office space have been going up at 4.8% per year compounded annually for the past 5 years.
If office space is now $35 per square foot, what were the rental rates 5 years ago?
Formula __________
Ans: _____________
6
Page 2A of 3
Q5: If $2,000 is deposited each quarter into an ordinary annuity paying 8% compounded quarterly,
A. Complete the balance sheet for the first three quarters.
period
deposit
interest
balance
1
2,000.00
0.00
2,000.00
2
3
B. When will the account have a value of $100,000?
Formula _______
Ans:_____________
12
Q6: The Hartford offered an annuity that pays 4.8% compounded monthly. What equal monthly deposit should be
made into this annuity in order to have $50,000 in 10 years?
Formula __________
Ans: _____________
6
Q7: A stock trading company charges a commission of $20 + 1% of the principal for both the purchase and sale of
stocks. An investor purchases 200 shares at $21.50 a share, holds the shares for 26 weeks, and then sells the
stock for $25.00 a share. Find the annual rate of interest earned with this investment.
Formula: ___________
Ans: _______________
10
Page 3A of 3
Q8: A retiree has an annuity that pays 5.6% compounded quarterly with a current balance of $30,000. He wants to
make equal quarterly withdrawals so that at the end of 5 years the account balance is $0.
A. What is the value of each withdrawal ?
B. How much interest was earned during the first year?
Formula __________
10
A. Ans: ________________
B. Ans: ________________
Q9: A family has a $150,000, 20 – year mortgage at 6% compounded monthly.
A. Complete the amortization table for the first two payments.
Period
Payment
interest
reduction on
unpaid balance
unpaid balance
16
0
0
1
1074.65
2
1074.65
0
0
150,000
B. After 5 full years of payments, what is the unpaid balance of the mortgage?
C. How much interest is paid during the 20 years?
Formula: ____________
B. Ans:_________________
C. Ans:_________________
Math 70 - Test #2B – Spring 09
8.5, Chapter 3
Score: _____
Row_____ Name__________________________________
80
Where appropriate, and whether or not you are using the MATH SOLVER, you must
 Name the formula
 List the values that are inserted into each of the formula's variables
 Box the variable that you solved for
 Place your labeled answer in the box to the right. Monetary values should be rounded to the nearest
penny. Other decimal answers should be rounded to three significant digits to the right of the decimal.
 If you are not using the MATH SOLVER, you may use scratch paper to do your calculations.
Q1: Expected Value: A card is drawn from a standard 52-card deck. If the card is an heart, you win $5;
otherwise, you lose $1. Set up the payoff table and find the expected value of the game to you.
𝑥𝑖
𝐸(𝑋) =____________
6
𝑝𝑖
Q2: What is the annual percentage yield for money invested at
A. 8% compounded continuously?
B. 8.1% compounded semiannually?
C. Which is the better investment? ______
A. Formula __________
Ans: ________________
8
B. Formula:__________
Ans:________________
Q3: At what annually compounded rate must money be invested,
if it is to double in 6 years ?
Formula __________
Ans: _____________
6
Q4: Rental costs for office space have been going up at 3.8% per year compounded annually for the past 5 years.
If office space is now $25 per square foot, what were the rental rates 5 years ago?
Formula __________
Ans: _____________
6
Page 2B of 3
Q5: A stock trading company charges a commission of $20 + 1% of the principal for both the purchase and sale of
stocks. An investor purchases 200 shares at $18.50 a share, holds the shares for 26 weeks, and then sells the
stock for $22.00 a share. Find the annual rate of interest earned with this investment.
Formula: ___________
Ans: _______________
10
Q6: If $4,000 is deposited each quarter into an ordinary annuity paying 8% compounded quarterly,
A. Complete the balance sheet for the first three quarters.
period
deposit
interest
balance
1
4,000.00
0.00
4,000.00
12
2
3
B. When will the account have a value of $100,000?
Formula _______
B. Ans:_____________
Q7: The Hartford offered an annuity that pays 5.5% compounded semiannually. What equal semi-annual deposit
should be made into this annuity in order to have $80,000 in 10 years?
Formula __________
Ans: _____________
6
Page 3B of 3
Q8: A retiree has an annuity that pays 5.2% compounded quarterly with a current balance of $30,000. He wants to
make equal quarterly withdrawals so that at the end of 5 years the account balance is $0.
A. What is the value of each withdrawal ?
B. How much interest was earned during the first year?
Formula __________
A. Ans: ________________
10
B. Ans: ________________
Q9: A family has a $200,000, 20 – year mortgage at 6% compounded monthly.
A.
Complete the amortization table for the first two payments.
Period
Payment
interest
reduction on
unpaid balance
0
0
0
0
1
1432.86
2
1432.86
16
unpaid balance
200,000
B. After 5 full years of payments, what is the unpaid balance of the mortgage?
C. C. How much interest is paid during the 20 years?
Formula: ____________
B. Ans:_________________
C. Ans:_________________