Effective Interest Rates
Reducing Balance Loan
Annuities
Graphs & Networks
Connector problems
100
How many fortnights in a year
26
100
$4800 is borrowed and charged compound interest at the rate of 15% per annum, compounding monthly. If the monthly repayments are $300 construct a recurrence relation model for this loan.
A0=4800, An+1= 1.0125An -300
100
A foundation invests $600 000 to provide a $500 per month award. Determine the interest rate required to support this perpetuity.
i=1% p.a.
100
How do I know if a graph is Semi-Eulerian?
There are exactly 2 vertices with odd degrees and the rest are even.
100
In a flow network problem, the minimum cut value represents what?
The maximum flow capacity.
200
What is the effective interest rate formula?
ieffective=((1+i/n)^n)-1
200
Recall the recursive model formula for reducing balance loans.
A(n+1) =rAn - R
200
Which annuities formula is used to calculate the future value of an investment or how much money to deposit to reach an investment goal.
A=M((1+i)^n)-1/i)
200
What are the dots (nodes) on a graph called?
Vertices
200
True or false:
A tree has no loops, multiple edges or cycles
True
300
A savings account advertises 6.8% p.a. compounding monthly. Determine the effective interest rate
7.02%
300
Use this recurrence relation to determine the balance of the loan after 2 payements.
A0=48000, An+1= 1.0125An -300
$4317
300
Calculate the future value of investing $150 every month for 10 years at 6.5% p.a. compounded quarterly. Round to the nearest dollar.
A=$25260.00
300
What are the lines of a graph called?
Edges
300
If a graph has 8 vertices, how many edges will its minimum spanning tree have?
7
400
A $25,000 car loan at 6% p.a. over 5 years has monthly repayments of $483.32. Calculate the total interest paid?
$3999.20
400
A loan of $6000 with monthly repayments of $200 has a balance of $5100 after 6 months. Determine the amount ($) of interested charged on the loan during this time.
$300
400
True or false:
A recurrence relation can be applied to a loan and investment annuity.
True
400
How can you determine whether a graph is Eulerian?
All vertices have an even degree (E for Even)
400
When completing the steps to solve the Hungarian algorithm, the graph used to assigned tasks is called what?
Bipartite graph
500
Justify which option would be better if a person was wanting to take out a $5,000 loan over 3 years.
Option A: 8% p.a. monthly or,
Option B: 8% p.a. weekly.
Option A = 8.2999%
Option B = 8.322%
As it is a loan, the interest rate should be low to reduce amount of interest to pay. Therefore, option A has the smaller effective interest rate of 8.2999%
500
$8400 is borrowed with interest charged at 11.4% per annum, compounding monthly with monthly repayments of $500.
Determine the balance of the loan after 5 repayments.
$6258.70
500
A retirement plan offers $1,200/month for 25 years. If interest is 5% p.a. compounded monthly, how much is needed today?
Round to the nearest whole dollar.
A=$205272
500
Define/ explain the difference between:
Path
Trail
Walk
Path - no repeated vertices or edges
Trail - no repeated edges but can repeat vertices
walk - can repeat vertices and edges
500
Construct a project network to identify the critical path and how long to complete the project.
Critical Path = A, B, C, E, F, G
Minimum completion time = 29 minutes