Networks
What is the name of the table used to show which vertices are connected?
Adjacency matrix
Future Value
Convert 7.3% compounded monthly to a monthly interest rate
0.6083%
A graph has every vertex with an even degree.
What type of graph could it be?
Eulerian
Compound Interest
Future Value
Present Value
Which involves regular repayments?
Present Value
A graph has
8 vertices
12 edges.
What is the degree of Vertex A if four edges are connected to it?
Ans:4
Single lump sum investment.
No additional deposits.
Which model?
Compound Interest
If a loan is taken out over 8 years. How many monthly repayments will this be?
96 payments
How many vertices of odd degree does a Semi-Eulerian graph have?
Exactly 2
True or False
A graph can be weighted and directed.
True
True or False
The adjacency matrix for an undirected graph is symmetrical.
TRUE
A home loan required regular repayments. Which model would you use.
Present Value
A bank advertises two investments accounts
A: 5.8% p.a. compounded annually
B: 5.7% p.a. compounded monthly
A student says that option A is better because it has the higher advertised interest rate. Is the student's reasoning valid?
Not necessarily valid, you will need to look at the effective annual rate.
Which type of path visits every vertex exactly once?
Hamiltonian Path
A person deposits $250 each month into a savings account.
Which financial model should they use?
Future Value Annuity
Name two features of a weighted graph.
Present Value
A principal of $14 000 is invested and will earn compound interest at the rate of 2.8% per annum, compounding weekly. The effective annual rate of interest for this investment is closest to:
A 2.80%
B 2.81%
C 2.82%
D 2.83%
E 2.84%
Ans: E
Which type of graph travels every edge exactly once and finishes where it started?
Eulerian Graph (or Eulerian Circuit)
A student begins solving a question using Future Value Annuity, but the question is about a car loan.
Identify the mistake and explain what model should have been used.
The student selected the wrong financial model.
A car loan involves borrowing money and making regular repayments, so Present Value Annuity should be used.
Explain the difference between a weighted graph and an unweighted graph.
The main difference is that a weighted graph assigns a specific number, or weight, to each edge, while an unweighted graph treats all edges as equal
Explain why a car loan uses a Present Value Annuity
Regular repayments
Ian borrows $4000 from a bank. The bank will charge him interest at the annual rate of 9.8%.
Construct a recurrence relation model for the value of Ian's loan after n years.
A_0 = 4000, A_n+1 = 1.098 × A_n
A student says:
"A Hamiltonian graph must use every edge exactly once."
Is the student correct? Explain.
No
A Hamiltonian graph is concerned with visiting every vertex exactly once (returning to the start for a Hamiltonian cycle). Using every edge exactly once is the defining property of an Eulerian graph.
A road between two towns is closed.
Explain how this might affect the shortest path through a transport network.
The shortest path may change because travellers must use alternative routes, increasing the total distance or cost.