Assessment Task Sheet

Australian International Academy, Kellyville

Name: _____________________________ Date: _______________

Year Level: Year 10 Subject: Mathematics

TITLE: Financial Mathematics

Due Date: 6th March 2018

Part A

Compare the investment of $6000 earning 7.6% p.a. at both simple interest and compound interest over a five year period. Which is the better investment? Complete the table. Reflect on the relation between Simple Interest and Compound Interest and explain your finding. (Word Limit: 100 – 150 words)

Year Simple Interest Compound Interest1 $6000x7.6%x1= $456 $6000x7.6% x1= $4562 $6000x7.6%x1= $456 $6456x7.6%x1=$490.663 $6000x7.6%x1= $456 $6946.66x7.6%x1=$527.954 $6000x7.6%x1= $456 $7474.61x7.6%x1=$568.075 $6000x7.6%x1= $456 $8042.68x7.6%x1=$611.24

Amount at the end of five years

456x5= $2280+$6000=$8280

8042.68+611.24=$8653.92

As you can see compound interest gives you the better return

Part A reflection: -

Part A was an easier part and less time consuming in comparison to part b due to the fact that part a didn’t require any research it only required calculations. Where as part b, had required calculations and research. I found this relatively easy due to we have done this in class it was just the fact that you had to get the calculations right, if you hadn’t for one of them then the whole calculation is done. Overall this assessment was a bit challenging in some areas but in some other areas it took me a bit to get my head around it but then I had figured it out.

Part B

Ali is a year 10 student. He worked at Discount Chemist during weekends last year. He was paid $15 per hour and he worked 20 hours per month for a whole year. He has decided to concentrate on his school work so he quit his weekend job.

He wants to go to Bali after his Yr 12 exams and so, he wants to invest all of his money into a savings account. Research three different banks to find out their interest rates. Where would you advice Ali to invest in order to maximise his

savings if he invests for a period of 2.5 years. Please show evidence of your research.

the ANZ premium cash management account is not suitable for Ali as you have to have a minimum of $10,000 and Ali only has $3,600. The best option out of these is the first one as it gives him back a total of $3,829.5.

3600x2.55%x0.5= 45.90

3600x2.55%x1= 91.80

3600x2.55%x1.5= 137.70

3600x2.55%x2= 183.60

3600x2.55%x2.5= 229.50

In commonwealth the term deposits don’t work for Ali as again the minimum for that is $10,000, The one that gives me the best return is NetBank saver. The calculation I used to find out the amount after one year for NetBank saver is

3600x2.51%x0.5= $45.18

3600x2.51%x1= $90.36

3600x2.51%x1.5= $135.54

3600x2.51%x2= $180.72

3600x2.51%x2.5= $225.9.

Goal saver: -

Bump savings: -

In Westpac I have found that Westpac e-saver is the best out of three. You receive back a total of $3,825.9. I calculated this by

3600x2.51%x0.5= $45.18

3600x2.51%x1=$90.36

3600x2.51%x1.5= $135.54

3600x2.51%x2=$180.72

3600x2.51%x2.5= $225.9

Using Excel Software, draw a graph comparing the different compounding interest rates over the given time. Compound interest.

0 0.5 1 1.5 2 2.5 3$0.00

$50.00

$100.00

$150.00

$200.00

$250.00

comparison of banks

ANZ Westpac ComBank

This graph indicates that if Ali creates a savings account with ANZ bank he will maximise his profits, which is $3,829.50. As you can see the lines are very close to each other. Commonwealth Bank and Westpac are identical as they had the same interest rate.

Search the best deal for Ali if he wants to stay in Bali for 7 nights. The cost is based on airfares, airport transfer and accommodation. Please show evidence of your research from at least 2 different websites. If the inflation rate is __2.3%____ how much would Ali’s travel cost him? Reflect on how the inflation affects his savings. (Word Limit: 100 – 150 words)

Ali’s in total including flight and return which includes of 20kg luggage but has one stop into Melbourne, also food and entertainment for the price of $935. His flight to Bali is $543 multiplied by the inflation rate makes it 12.49. $12.49+$543=$555.49 for 2019 then for 2020 it will be 555.49 multiplied with inflation rate to get 12.78. $12.78+$555.49=$568.27. Same thing for his return will cost in 2020 is $410.24. The over all fare for his flight is $978.51. this now leaves him with $2850.99. Ali will be driving during his stay in Bali. He will pick it up and drop it back off at the airport. His car fee comes to $598.62 after the inflation rate. This now leaves Ali with a total of $2252.37. Ali’s accommodation consists of a free breakfast and it has a rating of 8.3 which is “very good”. The only thing this doesn’t have is Wi-Fi in the room, but besides that it is all relaxing and a very nice location. At the end of the calculation this will end up costing in 2020 comes to $376.75. at the end of all these expenses Ali would have $1875.62 to spend on food and souvenirs. In total at the end the expenses of the trip consisting of the accommodation, airfares, and transport (not including food and souvenirs) comes to $1953.88 when the inflation rate is initiated. When the inflation rate is not implemented the cost of the trip is $1867.

Reflection for part B:

In part B I actually found it interesting to be searching for all the requirements to be able to go on a holiday and have some fun but also by staying within a budget. The inflation rate had made everything a little more expensive which brought down Ali’s savings. This is ok as he had a good amount of money to spend while he is there. I also found it pretty interesting figuring out the amount of money Ali was getting back just for having it sitting in there. I had kept on getting confused in part 2 because I had keep forgetting to multiply the answer with the inflation rate so I had to keep going back and re-doing it. It was interesting to see how it is done and all the things you have to think about when booking a holiday.

Your Final Submission must include:

Part A:

- Completed table - Answer the Question - Which is the better investment? - Reflection (Check your word limit)

Part B:

- Calculating the principal- Calculating the best returns- Evidence of research for best returns (Snapshot for each bank)- Excel Graph- Evidence of research for best holiday deal(Snapshot for each website)- Final Travel Cost

- Reflection (Check your word limit)

BOS Outcomes:

MA5.2-1WM - selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.2-2WM - interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problemsMA5.1-3WM - provides reasoning to support conclusions that are appropriate to the context MA 5.1- 4NA - solves financial problems involving earning, spending and investing money MA5.2-4NA - solves financial problems involving compound interest

MYP Outcomes: Criteria A and D

Simple interest is one calculation compound interest is separated calculations.

Criterion A: Knowing and understanding

Achievement level Level descriptor Specific Task descriptor0 The student does not reach a

standard described by any of the descriptors below.

The student was unable to answer the questions and was unable to complete the task.

1 - 2 The student is able to:i. select appropriate

mathematics when solving simple problems in familiar situations

ii. apply the selected mathematics successfully when solving these problems

iii. generally solve these problems correctly.

Part A: The student is able to apply the formulae for simple and compound interest correctly.

Part B: The student is able to calculate the wages and its returns to a degree of accuracy

3 – 4 The student is able to:

i. select appropriate mathematics when solving more complex problems in familiar situations

ii. apply the selected mathematics successfully when solving these problems

iii. generally solve these problems correctly.

Part A: The student is able to calculate the amount at the end of the given period of time and able to identify the better investment.

Part B: The student is able to calculate the wages and its returns accurately.

5 - 6 The student is able to:

i. select appropriate mathematics when solving challenging problems in familiar situations

ii. apply the selected mathematics successfully when solving these problems

iii. generally solve these problems correctly.

Part B:The student is able to calculate the wages and its returns accurately and identify the best investment from their calculations.

7 - 8 The student is able to:i. select appropriate

mathematics when solving challenging problems in both familiar and unfamiliar situations

ii. apply the selected mathematics successfully when solving these problems

iii. generally solve these problems correctly.

Part B: The student is able to calculate the wages and its returns accurately and identify the best investment from their calculations and their excel graph.

Criterion D: Applying mathematics in real-life contexts

Achievement level Level descriptor Specific Task descriptor0 The student does not reach a

standard described by any of the descriptors below.

The student was unable to answer the questions and was unable to complete the task.

1 - 2 The student is able to:

i. identify some of the elements of the authentic real-life situation

ii. apply mathematical strategies to find a solution to the authentic real-life situation, with limited success.

Part A: The student is able to identify some elements of the relation between simple interest and compound interest.

Part B: The student does some research to find out the different interest rates / holiday deals and provides some evidence.

3 – 4 The student is able to:

i. identify the relevant

Part A: The student is able to identify the relation between simple interest and compound

elements of the authentic real-life situation

ii. select, with some success, adequate mathematical strategies to model the authentic real-life situation

iii. apply mathematical strategies to reach a solution to the authentic real-life situation

iv. discuss whether the solution makes sense in the context of the authentic real-life situation.

interest and explain it using mathematical terminologies.

Part B: The student does some research to find out the different interest rates / holiday deals and provides some evidence. The student is able to identify the best returns.

5 - 6 The student is able to:

i. identify the relevant elements of the authentic real-life situation

ii. select adequate mathematical strategies to model the authentic real-life situation

iii. apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation

iv. explain the degree of accuracy of the solution

v. explain whether the solution makes sense in the context of the authentic real-life situation.

Part A: The student is able to identify the relation between simple interest and compound interest and explain it using appropriate mathematical terminologies.

Part B: The student does extensive research to find out the different interest rates / holiday deals and provides evidence. The student is able to identify the best returns. The student makes the connection between inflation and the cost.

7 - 8 The student is able to: i. identify the

relevant elements of the authentic real-life situation

ii. select appropriate mathematical strategies to model the authentic real-life situation

Part A: The student is able to identify the relation between simple interest and compound interest, explain it using appropriate mathematical terminologies and reflect on it.

Part B: The student does extensive research to find out the different interest rates /

iii. apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation

iv. justify the degree of accuracy of the solution

v. justify whether the solution makes sense in the context of the authentic real-life situation.

holiday deals and provides evidence. The student is able to identify the best returns. The student makes the connection between inflation and the cost and uses appropriate mathematical terminologies in their reflection.

Do we have to add bonus rates in calculation?

Do you add your inflation rate to your final amount 2.3/100?

Do you add of minus inflation rate by final amount?

Can we just use simple interest for the calculation?