MAT 230 MOD 5, Summer 1 2015 Test #1 (Units 1, 2, 3, & 4) (Quiz)

| September 28, 2018

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Current
Score : – / 121 Due : Sunday, May 24 2015 11:59 PM EDT
1. –/1
pointsBerrFinMath1 2.1.001.
Find the
simple interest on the loan.
$1800 at
6% for 10 years.
$
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2. –/1
pointsBerrFinMath1 2.1.003.
Find the
total amount due for the simple interest loan.
$1600 at
7% for 10 years.
$
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3. –/2
pointsBerrFinMath1 2.2.001.
Determine
the amount due on the compound interest loan. (Round your answers to the
nearest cent.)
$15,000 at
5% for 15 years if the interest is compounded in the following ways.
(a)
annually
$
(b)
quarterly
$
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Test #1
(Units 1, 2, 3, & 4) (Quiz)

4. –/1
pointsBerrFinMath1 2.2.005.
Find the
term of the compound interest loan. (Round your answer to two decimal places.)
4.9%
compounded quarterly to obtain $8600 from a principal of $2000.
yr
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5. –/2
pointsBerrFinMath1 2.2.007.
Use the
“rule of 72” to estimate the doubling time (in years) for the
interest rate, and then calculate it exactly. (Round your
answers to
two decimal places.)
4%
compounded annually.
“rule
of 72” yr
exact
answer yr
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6. –/1
pointsBerrFinMath1 2.2.009.
Find the
effective rate of the compound interest rate or investment. (Round your answer
to two decimal places.)
21%
compounded monthly. [Note: This rate is a typical credit card interest rate,
often stated as 1.8% per month.]
%
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(Optional)
7. –/1
pointsBerrFinMath1 2.2.012.
You have
just received $125,000 from the estate of a long-lost rich uncle. If you invest
all your inheritance in a tax-free bond fund
earning
6.8% compounded quarterly, how long do you have to wait to become a
millionaire? (Round your answer to two decimal
places.)
yr
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8. –/1
pointsBerrFinMath1 2.2.014.
You have
just won $190,000 from a lottery. If you invest all this amount in a tax-free
money market fund earning 8%
compounded
weekly, how long do you have to wait to become a millionaire? (Round your
answer to two decimal places.)
yr
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9. –/1
pointsBerrFinMath1 2.3.001.
In the
following ordinary annuity, the interest is compounded with each payment, and
the payment is made at the end of the
compounding
period.
Find the
accumulated amount of the annuity. (Round your answer to the nearest cent.)
$1500
annually at 5% for 10 years.
$
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10.–/1
pointsBerrFinMath1 2.3.003.
In the
following ordinary annuity, the interest is compounded with each payment, and
the payment is made at the end of the
compounding
period.
Find the
required payment for the sinking fund. (Round your answer to the nearest cent.)
Monthly
deposits earning 6% to accumulate $4000 after 10 years.
$
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11.–/1
pointsBerrFinMath1 2.3.005.
In the
following ordinary annuity, the interest is compounded with each payment, and
the payment is made at the end of the
compounding
period.
Find the
amount of time needed for the sinking fund to reach the given accumulated
amount. (Round your answer to two decimal
places.)
$4500
yearly at 7% to accumulate $100,000.
yr
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12.–/2
pointsBerrFinMath1 2.3.007.
In the
following ordinary annuity, the interest is compounded with each payment, and
the payment is made at the end of the
compounding
period.
An
individual retirement account, or IRA, earns tax-deferred interest and allows
the owner to invest up to $5000 each year. Joe
and Jill
both will make IRA deposits for 30 years (from age 35 to 65) into stock mutual
funds yielding 9.3%. Joe deposits $5000
once each
year, while Jill has $96.15 (which is 5000/52) withheld from her weekly
paycheck and deposited automatically. How
much will
each have at age 65? (Round your answer to the nearest cent.)
Joe $
Jill $
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13.–/1
pointsBerrFinMath1 2.3.010.
In the
following ordinary annuity, the interest is compounded with each payment, and
the payment is made at the end of the
compounding
period.
You and
your new spouse each bring home $1500 each month after taxes and other payroll
deductions. By living frugally, you
intend to
live on just one paycheck and save the other in a mutual fund yielding 7.89%
compounded monthly. How long will it
take to
have enough for a 20% down payment on a $155,000 condo in the city? (Round your
answer to two decimal places.)
yr
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14.–/1
pointsBerrFinMath1 2.4.003.
Determine
the payment to amortize the debt. (Round your answer to the nearest cent.)
Monthly
payments on $130,000 at 3% for 25 years.
$
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15.–/1
pointsBerrFinMath1 2.4.005.
Find the
unpaid balance on the debt. (Round your answer to the nearest cent.)
After 7
years of monthly payments on $150,000 at 5% for 25 years.
$
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16.–/1
pointsBerrFinMath1 3.1.001.
Solve the
system by graphing. (Enter your answers as a comma-separated list. If the
system is inconsistent, enter
INCONSISTENT.
If the system is dependent, enter DEPENDENT.)
=
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x + y = 8
x ? y = 2
(x, y)

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17.–/1
pointsBerrFinMath1 3.1.003.
Solve the
system by the elimination method. (Enter your answers as a comma-separated
list. If the system is inconsistent, enter
INCONSISTENT.
If the system is dependent, enter DEPENDENT.)
=
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18.–/2
pointsBerrFinMath1 3.1.008.
Formulate
the situation as a system of two linear equations in two variables. Be sure to
state clearly the meaning of your x- and
y-variables.
Solve the system by the elimination method. Be sure to state your final answer
in terms of the original question.
A lawyer
has found 60 investors for a limited partnership to purchase an inner-city
apartment building, with each contributing
either
$6,000 or $12,000. If the partnership raised $504,000, then how many investors
contributed $6,000 and how many
contributed
$12,000?
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19.–/4
pointsBerrFinMath1 3.2.001.
Find the
dimension of the matrix.
?
Find the
values of the specified elements.
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x + y = 6
2x + 3y =
14
(x, y)
x = $6,000
investors
y =
$12,000 investors
8 5
5 1
3 9
a1,1 =
a3,2 =

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20.–/6
pointsBerrFinMath1 3.2.003.
Find the
augmented matrix representing the system of equations.
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Work (Optional)
21.–/6
pointsBerrFinMath1 3.2.005.
Carry out
the row operation on the matrix.
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Work (Optional)
22.–/6
pointsBerrFinMath1 3.2.006.
Carry out
the row operation on the matrix.
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Work (Optional)
x + 5y = 5
3x + 7y =
15

R1 ? R2 on
4 8 25
6 2 27

R1 ? R2 ?
R1 on 9 8 51
4 6 59

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23.–/6
pointsBerrFinMath1 3.2.007.
Carry out
the row operation on the matrix.
Show My
Work (Optional)
24.–/1
pointsBerrFinMath1 3.2.008.
Interpret
the augmented matrix as the solution of a system of equations. (Enter your
answers as a comma-separated list. If the
system is
inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
=
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Work (Optional)
25.–/2
pointsBerrFinMath1 3.2.015.
Express
the situation as a system of two equations in two variables. Be sure to state
clearly the meaning of your x- and yvariables.
Solve the
system by row-reducing the corresponding augmented matrix. State your final
answer in terms of the original
question.
For the
final days before the election, the campaign manager has a total of $45,000 to
spend on TV and radio campaign
advertisements.
Each TV ad costs $3000 and is seen by 10,000 voters, while each radio ad costs
$500 and is heard by 2000
voters.
Ignoring repeated exposures to the same voter, how many TV and radio ads will
contact 160,000 voters using the
allocated
funds?
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R2 ? R2 on
1
6
3 ?5 ?40
0 6 150

1 0 3
0 1 ?9
(x, y)
x = TV ads
y = radio
ads

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26.–/12
pointsBerrFinMath1 3.3.001.
Find the
augmented matrix representing the system of equations.
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Work (Optional)
27.–/1
pointsBerrFinMath1 3.3.003.
Interpret
the row-reduced matrix as the solution of a system of equations. (Enter your
answers as a comma-separated list. If the
system is
inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the
solutions in terms of the parameter
t.)
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Work (Optional)
x1 + x2 +
x3 = 3
x1 + 5×2 +
x3 = 2
x1 + 2×2 +
4×3 = 2

1 0 0 6
0 1 0 6
0 0 1 ?3
(x1, x2,
x3) =

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28.–/12
pointsBerrFinMath1 3.3.007.
Use an
appropriate row operation or sequence of row operations to find the equivalent
row-reduced matrix.
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29.–/9
pointsBerrFinMath1 3.4.002.
Use the
given matrix to find the expression.
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30.–/9
pointsBerrFinMath1 3.4.004.
Use the
given matrices to find the expression.
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Work (Optional)
1 0 1 6
0 1 0 2
0 0 1 3

C = ; 3C
9 6 2
2 2 7
5 9 4
3C =

A = C = ;
A + C
7 2 8
7 9 9
6 3 7
7 8 3
3 3 3
1 8 7
A + C =

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31.–/2
pointsBerrFinMath1 3.4.007.
Find the
matrix product.
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32.–/15
pointsBerrFinMath1 3.4.009.
Rewrite
the system of linear equations as a matrix equation AX = B.
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33.–/7
pointsBerrFinMath1 4.1.008.
Formulate
the situation as a system of inequalities. (Let x represent the number of
dinghies the company can manufacture and y
represent
the number of rowboats.)
A boat
company manufactures aluminum dinghies and rowboats. The hours of metal work
and painting needed for each
are shown
in the table, together with the hours of skilled labor available for each task.
How many of each kind of boat can
the
company manufacture?
(hours)
Dinghy Rowboat Labor Available
Metal Work
2 3 102
Painting 2
2 90
1 3 1
3 4 3
1
?4
5
x1 + 5×2 +
5×3 = 5
x1 + x2 +
x3 = 3
4×1 + 3×2
+ 2×3 = 8

=

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Sketch the
feasible region.
Find the
vertices. (Order your answers from smallest to largest x, then from smallest to
largest y.)
(labor for
metal work)
(labor for
painting)
x ? 0, y ?
0
(x, y)
=

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34.–/1
pointsBerrFinMath1 4.2.006.
Solve the
linear programming problem by sketching the region and labeling the vertices,
deciding whether a solution exists, and
then
finding it if it does exist. (If an answer does not exist, enter DNE.)
C =
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(x, y) =
(x, y) =
(x, y) =
Minimize C
= 15x + 75y
Subject to
2x + 5y ? 20
x ? 0, y ?
0

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