MATH 1300: Finite Mathematics
EXAM 1
20 September 2016
NAME:
.........................................................................
SECTION:
.........................................................................
INSTRUCTOR:
.........................................................................
SCORE
Correct
(A):
/15 =
%
INSTRUCTIONS
1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All exam pages must remain stapled.
Do not separate or remove any pages. You will have 60 minutes to complete this exam.
2. This exam has 10 pages, including the cover sheet. There are 15 multiple choice questions. The answers on your scantron
are your FINAL answers. If you change an answer, erase your old answer thoroughly. Only final answers on your scantron
will be graded.
3. Some potentially helpful formulas can be found on page 10.
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
2
MULTIPLE CHOICE: Mark your FINAL answers on your scantron.
1. If you invest $3000 on January 1, 2019 at 4% interest compounded quarterly, how much will you have on July 1,
2022? (Answers are rounded to the nearest cent.)
a
$2609.89
b
$3448.42
c
$5195.03
d
$4803.10
e
$3380.48
2. An amount of $5000 is deposited into a savings account at 3% interest compounded quarterly. How much interest
is earned during the first two years? (Answers are rounded to the nearest cent.)
a
$307.99
b
$1333.85
c
$304.50
d
$290.12
e
$75.28
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
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3. On January 1, 2006, a deposit was made into a savings account paying interest compounded semiannually. The
balance on January 1, 2009 was $10,000 and the balance on July 1, 2009 was $10,150. How large was the deposit?
(Answers are rounded to the nearest cent.)
a
$9282.60
b
$9151.42
c
$9100.00
d
$9288.69
e
$9145.42
4. Consider a $100,075, 30-year mortgage at interest rate 6% compounded monthly with a $600 monthly payment.
What is the unpaid balance at the end of 25 years? (Answers are rounded to the nearest cent.)
a
$14,067.38
b
$93,124.12
c
$62,079.73
d
$31,035.34
e
None of the above
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
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5. If someone 20 years old deposits $3000 each year into a savings account for 50 years at 5% interest compounded
annually, how much money will be in the account when this person retires at age 70? (Answers are rounded to
the nearest cent.)
a
$659,710.15
b
$219,991.95
c
$547,677.76
d
$628,043.99
e
None of the above
6. Using the add-on method, what is the monthly payment for a $7000 loan at 6% interest for three years? (Answers
are rounded to the nearest cent.)
a
$212.95
b
$195.42
c
$229.44
d
$197.36
e
None of the above
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
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7. A loan of $105,501.50 is to be amortized over a 5-year term at 6% interest compounded monthly with monthly
payments and a $30,000 balloon payment at the end of the term. What is the monthly payment for this loan?
(Answers are rounded to the nearest cent.)
a
$1609.66
b
$1843.18
c
$1650.18
d
$2036.18
e
$1459.66
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
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8. Consider a 30-year $150, 000 5/1 ARM having a 2.4% margin and based on the CMT index. Suppose the interest
rate is initially 6% and the value of the CMT is 4.9% five years later. Assume that all interest rates use monthly
compounding. What is the monthly payment for the first 5 years? (Answers are rounded to the nearest cent.)
a
$2899.92
b
$2823.82
c
$584.91
d
$899.33
e
$796.09
9. For the mortgage in question 8, what is the monthly payment for the 6th year? (Answers are rounded to the
nearest cent.)
a
$619.18
b
$807.86
c
$2627.70
d
$2783.69
e
$1013.41
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
10. Use the Gauss-Jordan elimination method to find all solutions for the following system of equations:
x + 3y = 8
4x + 3y = 5
1
3
a
x = 5, y =
b
x = −19, y = 9
c
x = −1, y = 3
d
x = 8 − 3y, y = any real number
e
There are no solutions.
11. Use the Gauss-Jordan elimination method to find all solutions of the system of equations:


x + 2y =
5
−2x + 2y = −4

−x + 5y =
2
a
x = 5 and y = 1
b
x = 3 and y = 1
c
x = 5 − 2y and y = any real number
d
x = 5 + 2y and y = any real number
e
There are no solutions.
7
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
12. Use the Gauss-Jordan elimination method to find all solutions of the system of equations:

z = −1
 −x + y +
−x + 4y − 11z = −19

6x − 5y − 10z =
0
a
x = −5, y = −4, z = 0
b
x = −5, y = −6, z = 0
c
x = −5 + 5z, y = −6 + 4z, z = any real number
d
x = −5 − 5z, y = −4 + 6z, z = any real number
e
There are no solutions.
13. Perform matrix multiplication (if possible):
4 −1
0 −3
15 3
−3 17
16 2
0 15
17 −3
3 15
16 −40
0
0
b
c
e
a
d
4 −2
−1 −5
It is not possible to multiply these matrices.
8
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
(A)
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Questions 14-15: Statistics show that at a certain university, 70% of the students who live on campus
during a given semester will remain on campus the following semester, and 90% of students living off
campus during a given semester will remain off campus the following semester.
Let x and y denote the number of students who live on and off campus this semester, and let u and
v be the corresponding numbers for the next semester. Then the following system of equations can be
formed.
0.7x + 0.1y = u
0.3x + 0.9y = v
Suppose that 21,000 students currently live on campus and 12,000 currently live off campus.
14. How many students lived on campus last semester?
a
15,900
b
29,500
c
19,300
d
22,700
e
None of the above
15. How many students will live off campus next semester?
a
17,100
b
14,400
c
3500
d
10,300
e
None of the above
MATH 1300 Fall 2016 Exam 1: Name.........................................................................
Potentially Helpful Formulas
F = (1 + i)n P
P =
F
(1 + i)n
reff = APY = (1 + i)m − 1
F =
(1 + i)n − 1
·R
i
P =
1 − (1 + i)−n
·R
i
R=
P (1 + rt)
12t
(A)
10