WorksheetsGeneral Mathematics Unit 4
Total questions: 37
Worksheet time: 42mins
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
The starting value of this investment (n=0) is:
(a)
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
The percentage rate for this investment is:
(a)
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
The balance of this account after 1 year (n = 1) is:
(a)
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
The amount of interest earned after one year is:
(a)
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
The amount of interest after one year is $201. Therefore $201 is (a) % of $3000.
A recurrence relationship is given below.
An + 1 = 1.067An, A0 = $3000
Calculate when the balance will be above $5000
n = (a) ?
$10,000 compounds daily at 3% interest p.a.
Calculate the value after 6 months. (rounded to two decimal places)
(a)
Mr. Roweno Gonzales deposits in BDO at 2.4% per annum compounded monthly. What is his effective Annual rate?
2.43%
2.42%
2.46%
2.45%
What IS the effective interest rate?
An effect of interest
Compound interest turned into a simple interest rate for the year
The percentage increase over a year
A formulaic version of future values
Complete networks are networks where the vertices are all connected to each other.
If you were asked to compare different investment options that compound at different intervals, and justify your answer, how you would do that?
Use effective interest rate
Use an example amount and time, such as $1000 and 1 year, and show calculations
Look at the numbers and write some sentences
Bees
What letter represents "Future Value"?
A
P
I
i
n
A recurrence relationship is shown below:
An+1 = rAn - R, A0 = a
Does this show a reducing balance loan or a growing investment?
Reducing balance loan
Growing investment
A recurrence relationship is shown below:
An+1 = 1.08An - 100, A0 = 2000
Assume n is in months.
What is the interest rate per year?
(a)
A recurrence relationship is shown below:
An+1 = 1.08An - 100, A0 = 2000
Assume n is in months.
How much are the monthly repayments?
(a)
A recurrence relationship is shown below:
An+1 = 1.08An - 100, A0 = 2000
Assume n is in months.
How long until the loan is repayed?
10
20
30
40
Never
A recurrence relationship is shown below:
An+1 = 1.08An - 500, A0 = 2000
Assume n is in months.
How long until the loan is repayed?
6
3
9
12
Never
Ms James also wants some dragon horns. She took out a loan of $5000 at 24% p.a. She has monthly repayments of $200. Which of these is the recurrence relationship:
An+1 = 1.24An, A0 = 5000
An+1 = 1.02An - 200, A0 = 5000
An+1 = 1.24An - 200, A0 = 5000
An+1 = 1.24An - 2400, A0 = 5000
A recurrence relationship is shown below:
An+1 = rAn + R, A0 = a
Does this show a reducing balance loan or a growing investment?
Reducing balance loan
Growing investment
Ms James' great aunt Ahm naught A'widtch passed away, leaving her a single 1kg gold bar: $81,000. Ms James sells the bar and invests it into an account that compounds semi-annually, with a growth rate of 2% p.a.. She also adds $300 of her own money every month.
Which of these recurrence relationships
An+1 = 1.02An + 300, A0 = 81 000
An+1 = 1.01An + 300, A0 = 81 000
An+1 = 1.01An + 1800, A0 = 81 000
An+1 = 1.01An - 1800, A0 = 81 000
Ms James' great aunt Ahm naught A'widtch passed away, leaving her a single 1kg gold bar: $81,000. Ms James sells the bar and invests it into an account that compounds semi-annually, with a growth rate of 2% p.a.. She also adds $300 of her own money every month.
If Ms James kept the gold bar for 3 years, it would have sold for approximately $95000. Which of the two options would be better and why?
Keep the gold bar. The investment is only worth $88 909 in 3 years.
Sell now and invest. She would have a grand total of $97 057, which is higher than the value of the gold bar.
Keeping the gold bar. The total would be less than the value of the investment, but she wouldn't have to pay $10 800 in payments.
The investment. She should have $146 520 after 3 years.
$20,000 is borrowed over 210 days, compounding weekly, with monthly repayments, and a rate of 17.5% per annum. What units should the "i" and "n" be in?
Days
Weeks
Months
Years
Some people recommend you need $1, 000, 000 in savings to retire (through superannuation). If you had $1 million as a perpetuity, how much would you gain in interest per year if you were guaranteed 8% interest p.a. compounding monthly? (rounded to the nearest $1,000; no spaces or commas)
(a)
Following the previous question. Imagine you had a $1 million perpetuity. However, instead of 8% growth, it fell to 1% compounding monthly (similar to 2020). How much would you earn per year? (rounded to nearest $1000, no commas or spaces)
(a)
$200 is invested every week into an account that compounds monthly, at 5% interest p.a., for 3 years.
Which formula is the best/most efficient use to find the final value?
Compound Interest: A = P(1+i)n
Recurrence relation for annuities: An+1 = rAn + R
Annuities: A = M((1+i)n - 1)/i
Final Value: A = P + I
$200 is invested every week into an account that compounds monthly, at 5% interest p.a., for 3 years.
A = M((1+i)n - 1)/i
What units should n, i and M be in?
Days
Weeks
Months
Years
$200 is invested every week into an account that compounds monthly, at 5% interest p.a., for 3 years.
A = M((1+i)n - 1)/i
What is the final value? (Assume 4 weeks = month), (nearest 1000, no spaces or commas)
(a)
$200 is invested every week into an account that compounds monthly, at 5% interest p.a., for 3 years.
A = M((1+i)n - 1)/i = $31, 000
How much was paid into the account? (Assume 4x12 =48 weeks per year; yes this means there is some inaccuracies)
(a)
$200 is invested every week into an account that compounds monthly, at 5% interest p.a., for 3 years.
A = M((1+i)n - 1)/i = $31, 000, P = $28, 800
How much interest was earned?
(a)
A simple planar graph has an adjacency matrix with 5 rows and columns, the sum of values in the matrix is 14. How many vertices does the graph have?
(a)
A simple planar graph has an adjacency matrix with 5 rows and columns, the sum of values in the matrix is 14. How many edges does the graph have?
(a)
A simple planar graph has an adjacency matrix with 5 rows and columns, the sum of values in the matrix is 14. How many faces does the graph have?
(a)
What is a complete graph?
A graph that is completely drawn from the matrix
A graph where every vertex is connected to every other vertex
A graph with no loops or parallel arcs
A graph with no overlapping edges
When doing forward and backwards scans, you can find the minimum time to complete tasks. The numbers in the starting node and the finish node will always be the ______.
same
over 50
batman
really easy to calculate
Float time is...
the starting time of a project; when it is "floated".
the time when the proceeding task starts
the difference between the two values in the node
the time the task can be delayed without affecting the finish time
The difference between a Eulerian and a semi-Eulerian trail is...
One is every edge and one is every vertex
One starts and ends at the same vertex, the other doesn't.
One starts and ends at the same edge, the other doesn't.
Closed versus open
Below are the steps of the Hungarian Algorithm. What is the priority of the steps listed below:
X. Subtract the column minimum from each column.
Y. Subtract the row minimum from each row.
Z. Find the smallest uncovered number. Subtract it from all uncovered elements and add to all elements that are covered twice
(i.e. What should X, Y and Z be?)
2, 1, 3
1, 2, 3
3, 2, 1
3, 1, 2
What method is best for finding the shortest distance between different locations?
Hungarian Algorithm
Spanning trees
Bipartite graphs
Min cut, max flow
Planar graphs
