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Brief for the individual Project 1
Having learned how to model linked accounts, you are now well equipped to investigate
more realistic scenarios with several accounts and more diverse financial activities.
Consider a recent graduate who has
1. a student loan (with at least 3 years’ worth of fees),
2. an interest-bearing current account,
3. a job that pays a salary,
4. a car loan, and
5. some living expenses.
General information
Your mark for this assignment will contribute 30% to your final mark for the MA1691.
modular block. The assignment consists of 10 tasks, labelled (P1), (P2), (P3), (S1),
(S2), (S3), (D), (C1), (C2) and (C3). The total number of marks is 100, including
marks for the quality of the text and the typesetting.
The assignment must be typewritten, using the equation editor for the typesetting of the mathematics. The report must be submitted on-line, it should be
prepared in a form suitable for printing. In particular, it must be optimised for A4 sized
paper; the minimum font size is 11pt. The length of your report is capped at 4 pages
with minimum margins of 2cm. The report has to be submitted as a single .PDF file
submitted as the main document. Assessment for all components of this assignment
will include the quality of writing and typesetting. The Matlab files, and any additional
file(s), have to be uploaded as a WISEflow attachment in the form of a SINGLE zipped
folder named after your student number.
The DEADLINE to submit your report is
17:00 on Friday 19th May 2022 (Week 12).
MA1607 Project 1 -37-
Seminar session 4: Brief for the individual Project 1
As the rough estimate, your report should contain about 500 words. Try to be
concise and avoid including unnecessary details. When in doubt, please ask. You need
to reference the non-trivial information you use (which book, website or A-Level notes,
who did you ask etc.). What is important is to be candid about where your information
comes from, not to let the reader believe you did something you did not.
Individual parameters
To give most of you different numerical values to work with, note that the values of
the various parameters in the assignment are determined individually for you on the
basis of your student number. In the assignment,
• take the last three digits of the your student number. If any of these digits is 0,
replace it with 1.
• Now arrange them in increasing order, and call them u, v, and w in that order
(u is the smallest, w is the largest).
For example, if your student number is 2187604, then the last three digits are 604,
and in this case u = 1, v = 4 and w = 6.
Extenuating Circumstances (ECs), penalties for late submission and
plagiarism
Please note that the University enforces a very strict Policy for Coursework Submission,
as detailed here:
https://www.brunel.ac.uk/about/quality-assurance/documents/pdf/
Coursework-Submission-Policy.pdf
Please remember that this is an individual assignment. Group discussions are
healthy and encouraged; however, the work you submit must be your own and MUST
NOT BE prepared in collaboration with others.
MA1607 Project 1 -38-
Seminar session 4: Brief for the individual Project 1
Deliverables and requirements for the individual
assignment
The individual assignment for this project requires you to produce and submit two sets
of deliverables:
1. A report of no more than 4 pages (minimum font size 11pt and minimum margins
of 2cm; you can create your report in Microsoft Word, but it has to be submitted
as a single .pdf document). The report must contain
a) information on what you did change in the programme;
b) your two scenarios (see below);
c) your answers to the challenge questions;
d) the graphs relevant to your project;
e) an assessment on the strengths and weaknesses of your simulations;
2. All Matlab files you have modified or created (with comments).
The assignment tasks
This assignment starts with the code tracking1_2022.m that was released during
Lab 4.
(P) Your first set of tasks is to modify tracking1_2022.m to achieve the following:
P1 (worth 10%) Assume that in addition to the student loan and the current
account (already implemented in the program), you have a car loan, which
attracts interest, and on which regular payments have to be made from the
current account. Modify the program to include this new loan account, and
to link it appropriately with the current account.
P2 (worth 10%) In addition, make appropriate modification to the program so
as to have monthly living expenses paid regularly from the current account.
Modify the constants in the program to the following values determined
from your student number (the values of u, v, w were determined earlier):
i. the starting balance of the current account is £v, 000;
ii. the current account attracts annual nominal rate of (v/2)%, which is
compounded monthly;
iii. your monthly living expenses are £wuv;
iv. your salary is £10, 000 + uv, 000;
v. the initial car loan is for £1w, v00 with the annual nominal interest rate
of v% (compounded monthly) and the monthly repayment is £vw0;
vi. the RPI is 2.v%.
Run the programme for 15 years and plot the balance of the accounts as
months progress.
MA1607 Project 1 -39-
Seminar session 4: Brief for the individual Project 1
P3 (worth 10%) The plot produced by the program tracking1_2022.m is
very basic; your task here is to modify the program to add to the generated
plot a title, axes labels, and a legend, as well as employ different colours
and line types to visually distinguish different accounts.
(S) Your second set of tasks is to create, investigate and describe ONE realistic
scenario with an outcome different from P2 (worth 20%).
S1 To create a scenario means to select the values of all parameters of the model:
the principal, the salary, the value of the car loan, various interest rates,
etc. Replace the student loan with a housing loan, which attracts interest,
and on which regular payments have to be made from the current account.
The scenario has to be realistic, i.e. your data must be ’real’, and it must be
justified by reference to websites or other publications. For instance, find
out what the typical earnings are for your favourite job once you graduate,
how much a car/flat costs that you can afford on that salary, what the
typical interest rates are at your bank etc. You are encouraged to explore
websites dedicated to business, economics, and statistics. Government and
bank webpages are a good source as well.
S2 Your two scenarios P2 and S2 must display different outcomes, meaning
that the balance of at least one account must show qualitatively different
behaviour (increasing, decreasing or stationary) depending on the scenario.
S3 To investigate your two scenarios you need to simulate them for the appropriate number of years. In task P2 you had to simulate the accounts for
15 years, in this task you must simulate the accounts for 30 years. In each
case you should get the program to automatically plot the history of the
balances of all three accounts onto the same figure.
If you find that one or more of your plots is visually unbalanced (for example,
one of the accounts grows so large that the behaviour of the other two
accounts cannot be distinguished at the bottom of the graph), consider
producing additional plots highlighting different time windows, or a subset
of the accounts, in each case clearly explaining what you do and why.
(D) (worth 10%) Discuss the strengths and limitations of the assumptions underlying
your program. What features in it are not realistic? How would you modify it to
include additional features? Describe at least two specific additional features or
changes, and outline, in sufficient technical detail, how they can be implemented
in your code.
MA1607 Project 1 -40-
Seminar session 4: Brief for the individual Project 1
(C) Challenge questions.
C1 (Programming task, worth 10%.) Select a scenario in which the car loan is
fully paid off. Modify the iteration loop part of the program to answer the
following questions:
i. What is the exact amount of the final payment of the car loan?
ii. After how many months exactly is the car loan repaid?
Modify the programme so that the answers to those two questions are part
of the output.
C2 (Programming task, worth 10%) Answer the following question using your
modified program from task P: If the initial account balance is £ v, 000, how
many months are required to accumulate a balance in the current account
that would be sufficient to make a downpayment on a mortgage in the
amount of £x x, 000, where x is the fourth digit of your student number (if
this digit is 0, replace it with 1).
C3 (Analytical task, worth 10%.) Introduce the following modifications into the
scenario in task P, keeping all other parameters (such as car loan, student
loan payments, etc.) unchanged:
• set the initial balance of the current account to be £(5, 000 + 500 · v),
• set the monthly living expenses to be £1, u00.
Derive analytically the formula that determines the threshold salary such
that the current account value stays constant month after month during the
lifetime of the car loan after all monthly deposits and payments are made.
Include this derivation and the resulting formula into your report, and also
compute and report what the resulting salary is in your case.
(W) (worth 10%) Quality of the written presentation. Your written submission must
contain a clear and coherent text describing your scenarios, the justification for
them, and the simulation results. Clarity, organisation of the text, and quality of
English will all contribute to this part of the grade.
MA1607 Project 1 -41-
Brief for the individual Project 1
Having learned how to model linked accounts, you are now well equipped to investigate
more realistic scenarios with several accounts and more diverse financial activities.
Consider a recent graduate who has
1. a student loan (with at least 3 years’ worth of fees),
2. an interest-bearing current account,
3. a job that pays a salary,
4. a car loan, and
5. some living expenses.
General information
Your mark for this assignment will contribute 30% to your final mark for the MA1691.
modular block. The assignment consists of 10 tasks, labelled (P1), (P2), (P3), (S1),
(S2), (S3), (D), (C1), (C2) and (C3). The total number of marks is 100, including
marks for the quality of the text and the typesetting.
The assignment must be typewritten, using the equation editor for the typesetting of the mathematics. The report must be submitted on-line, it should be
prepared in a form suitable for printing. In particular, it must be optimised for A4 sized
paper; the minimum font size is 11pt. The length of your report is capped at 4 pages
with minimum margins of 2cm. The report has to be submitted as a single .PDF file
submitted as the main document. Assessment for all components of this assignment
will include the quality of writing and typesetting. The Matlab files, and any additional
file(s), have to be uploaded as a WISEflow attachment in the form of a SINGLE zipped
folder named after your student number.
The DEADLINE to submit your report is
17:00 on Friday 19th May 2022 (Week 12).
MA1607 Project 1 -37-
Seminar session 4: Brief for the individual Project 1
As the rough estimate, your report should contain about 500 words. Try to be
concise and avoid including unnecessary details. When in doubt, please ask. You need
to reference the non-trivial information you use (which book, website or A-Level notes,
who did you ask etc.). What is important is to be candid about where your information
comes from, not to let the reader believe you did something you did not.
Individual parameters
To give most of you different numerical values to work with, note that the values of
the various parameters in the assignment are determined individually for you on the
basis of your student number. In the assignment,
• take the last three digits of the your student number. If any of these digits is 0,
replace it with 1.
• Now arrange them in increasing order, and call them u, v, and w in that order
(u is the smallest, w is the largest).
For example, if your student number is 2187604, then the last three digits are 604,
and in this case u = 1, v = 4 and w = 6.
Extenuating Circumstances (ECs), penalties for late submission and
plagiarism
Please note that the University enforces a very strict Policy for Coursework Submission,
as detailed here:
https://www.brunel.ac.uk/about/quality-assurance/documents/pdf/
Coursework-Submission-Policy.pdf
Please remember that this is an individual assignment. Group discussions are
healthy and encouraged; however, the work you submit must be your own and MUST
NOT BE prepared in collaboration with others.
MA1607 Project 1 -38-
Seminar session 4: Brief for the individual Project 1
Deliverables and requirements for the individual
assignment
The individual assignment for this project requires you to produce and submit two sets
of deliverables:
1. A report of no more than 4 pages (minimum font size 11pt and minimum margins
of 2cm; you can create your report in Microsoft Word, but it has to be submitted
as a single .pdf document). The report must contain
a) information on what you did change in the programme;
b) your two scenarios (see below);
c) your answers to the challenge questions;
d) the graphs relevant to your project;
e) an assessment on the strengths and weaknesses of your simulations;
2. All Matlab files you have modified or created (with comments).
The assignment tasks
This assignment starts with the code tracking1_2022.m that was released during
Lab 4.
(P) Your first set of tasks is to modify tracking1_2022.m to achieve the following:
P1 (worth 10%) Assume that in addition to the student loan and the current
account (already implemented in the program), you have a car loan, which
attracts interest, and on which regular payments have to be made from the
current account. Modify the program to include this new loan account, and
to link it appropriately with the current account.
P2 (worth 10%) In addition, make appropriate modification to the program so
as to have monthly living expenses paid regularly from the current account.
Modify the constants in the program to the following values determined
from your student number (the values of u, v, w were determined earlier):
i. the starting balance of the current account is £v, 000;
ii. the current account attracts annual nominal rate of (v/2)%, which is
compounded monthly;
iii. your monthly living expenses are £wuv;
iv. your salary is £10, 000 + uv, 000;
v. the initial car loan is for £1w, v00 with the annual nominal interest rate
of v% (compounded monthly) and the monthly repayment is £vw0;
vi. the RPI is 2.v%.
Run the programme for 15 years and plot the balance of the accounts as
months progress.
MA1607 Project 1 -39-
Seminar session 4: Brief for the individual Project 1
P3 (worth 10%) The plot produced by the program tracking1_2022.m is
very basic; your task here is to modify the program to add to the generated
plot a title, axes labels, and a legend, as well as employ different colours
and line types to visually distinguish different accounts.
(S) Your second set of tasks is to create, investigate and describe ONE realistic
scenario with an outcome different from P2 (worth 20%).
S1 To create a scenario means to select the values of all parameters of the model:
the principal, the salary, the value of the car loan, various interest rates,
etc. Replace the student loan with a housing loan, which attracts interest,
and on which regular payments have to be made from the current account.
The scenario has to be realistic, i.e. your data must be ’real’, and it must be
justified by reference to websites or other publications. For instance, find
out what the typical earnings are for your favourite job once you graduate,
how much a car/flat costs that you can afford on that salary, what the
typical interest rates are at your bank etc. You are encouraged to explore
websites dedicated to business, economics, and statistics. Government and
bank webpages are a good source as well.
S2 Your two scenarios P2 and S2 must display different outcomes, meaning
that the balance of at least one account must show qualitatively different
behaviour (increasing, decreasing or stationary) depending on the scenario.
S3 To investigate your two scenarios you need to simulate them for the appropriate number of years. In task P2 you had to simulate the accounts for
15 years, in this task you must simulate the accounts for 30 years. In each
case you should get the program to automatically plot the history of the
balances of all three accounts onto the same figure.
If you find that one or more of your plots is visually unbalanced (for example,
one of the accounts grows so large that the behaviour of the other two
accounts cannot be distinguished at the bottom of the graph), consider
producing additional plots highlighting different time windows, or a subset
of the accounts, in each case clearly explaining what you do and why.
(D) (worth 10%) Discuss the strengths and limitations of the assumptions underlying
your program. What features in it are not realistic? How would you modify it to
include additional features? Describe at least two specific additional features or
changes, and outline, in sufficient technical detail, how they can be implemented
in your code.
MA1607 Project 1 -40-
Seminar session 4: Brief for the individual Project 1
(C) Challenge questions.
C1 (Programming task, worth 10%.) Select a scenario in which the car loan is
fully paid off. Modify the iteration loop part of the program to answer the
following questions:
i. What is the exact amount of the final payment of the car loan?
ii. After how many months exactly is the car loan repaid?
Modify the programme so that the answers to those two questions are part
of the output.
C2 (Programming task, worth 10%) Answer the following question using your
modified program from task P: If the initial account balance is £ v, 000, how
many months are required to accumulate a balance in the current account
that would be sufficient to make a downpayment on a mortgage in the
amount of £x x, 000, where x is the fourth digit of your student number (if
this digit is 0, replace it with 1).
C3 (Analytical task, worth 10%.) Introduce the following modifications into the
scenario in task P, keeping all other parameters (such as car loan, student
loan payments, etc.) unchanged:
• set the initial balance of the current account to be £(5, 000 + 500 · v),
• set the monthly living expenses to be £1, u00.
Derive analytically the formula that determines the threshold salary such
that the current account value stays constant month after month during the
lifetime of the car loan after all monthly deposits and payments are made.
Include this derivation and the resulting formula into your report, and also
compute and report what the resulting salary is in your case.
(W) (worth 10%) Quality of the written presentation. Your written submission must
contain a clear and coherent text describing your scenarios, the justification for
them, and the simulation results. Clarity, organisation of the text, and quality of
English will all contribute to this part of the grade.
MA1607 Project 1 -41-