Compound Interest
Recall the compound interest formula
A=P(1+i)^n
Recall the recursive model formula for reducing balance loans.
A(n+1) =rAn - R
Recall the annuities formula [1] used for the deposit phase.
A=M((1+i)^n)-1/i)
What are the dots (nodes) on a graph called?
Vertices
True or false:
A tree has no loops, multiple edges or cycles
True
$2814.20
Use this recurrence relation to determine the balance of the loan after 2 payements.
A0=48000, An+1= 1.0125An -300
$4317
Recall the annuities formula [2] for the withdrawal phase
A=M(1-(1+i)^-n)/i)
What are the lines of a graph called?
Edges
If a graph has 8 vertices, how many edges will its minimum spanning tree have?
7
$5000 is invested for 4 years at 8% compounding monthly. Calculate the balance of the account after 4 years.
$6878.33
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
True or false:
An annuity for both deposit and withdrawal phase can be solved using a recurrence relation?
True
How can you determine whether a graph is Eulerian?
All vertices have an even degree (E for Even)
When completing the steps to solve the Hungarian algorithm, the graph used to assigned tasks is called what? (looks like shoe laces)
Bipartite graph
$10 000 is invested for 6 years with interest compounding monthly. Determine the per annum (pa) interest rate offered if the balance is $16 135.02 after the 6 years
8% pa
$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
If there is a principal amount existing in an account that is in withdrawal, with two formulas need to be combined to solve for the balance of the account?
Compound interest - annuity [1]
How do I know if a graph is Semi-Eulerian?
In a flow network problem, the minimum cut value represents what?
The maximum flow capacity.
$20 000 is invested at 4.5% p.a compounding monthly. Determine how long the money was invested for to reach a value of $22884.96
6 years or 72 months
$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
Rearrange the annuities formula [1] to find the value of M.
M=A/[annuity 1]
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
Miscellaneous:
"Be back in a Jiffy" is a common saying meaning to be back soon... what measurement of time is a jiffy?
1/100th of a second