MATH 114 QUANTITATIVE REASONING
SECTIONS 2, 6, AND 23 :: FALL 2011 :: TEST 4
NAME ____________________________
Please show all necessary work. As noted in class, you will lose a point if you do not begin appropriate problems with a list of variables.
 APR 
A  P 1 

n 

nY

A  PMT 


 APR 
 1

n 

APR
n
nY
1





P  PMT 


 APR 
1   1

n 

APR
n
 nY




1. If you put $45 into a savings account every month which has an APR of 4.2%, how much will you
have in the account at the end of 5 years?
2. If you purchase a car for $18,800, what is your monthly payment on a 5 year loan with an APR of
5.7%?
What is the total amount of money you spend on the car? How much of that is interest?
3. Breny and her husband borrowed $210,000 to purchase a home. With an APR of 5.25%
compounded monthly and a 30 year loan, their monthly mortgage payment came out to be $1159.63.
How much of their first mortgage payment went to pay off the balance of the loan?
4. June has a retirement account set up which has an APR of 4.8%, compounded monthly. June’s
daughter, who took MAT 114, has calculated that June will need to save $1,083,333.33 in order to
retire as she would like.
a) How long will it take June to save the amount she needs if she invests $950 every month?
b) If June waits to start investing until she is 40 (and plans on retiring at 65), how much must she
invest each month in order to reach her investment goal?
5. Let G be a graph with V = { j, k, l, m, n, o, p } and E = { {j, k}, {j, l}, {j, m}, {j, n}, {l, m}, {l, p}, {n, p} }
a) Draw G.
b) What is the order of G?
c) Is G connected?
d) What is the degree of j?
e) How many vertices in G have odd
degree?
6. Decide if each of the graphs below has an Euler circuit or not. Label them as E = has an Euler circuit,
N = no way, man.
___
___
___
___
___
7. For the graph to the right, use the Nearest Neighbor
algorithm to find a Hamilton circuit in the graph
starting at vertex E. List the vertices in the order they
are visited and state the total weight of the circuit.
A
70
61
36
B
E
22
30
13
58
20
11
13
C
D
8. Repeat the Nearest Neighbor algorithm on the graph above to find a Hamilton circuit in the graph
starting at vertex D. List the vertices in the order they are visited and state the total weight of the
circuit.
9. For the graph to the right, use the Sorted Edges
algorithm to find a Hamilton circuit in the graph. List
the vertices in the order they are visited and state the
total weight of the circuit.
A
.1
6
5
B
E
.8
2.6
.7
2
3
2.1
C
.6
D