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

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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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21.–/6

pointsBerrFinMath1 3.2.005.

Carry out

the row operation on the matrix.

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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.

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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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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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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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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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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