[2022] Brunel - MA1607 Programming and Mathematical Projects - Compound Interest and Financial Planning
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.
The assignment tasks
This assignment starts with the code tracking1_2022.m that was released during Lab 4 (Week 9).
(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
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. 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 costs that you can afford on that salary, what the typical interest rates are at your bank, the typical monthly rent for a reasonable accommodation, etc. To get you started, check salaries on http://www.totaljobs.com/salary-checker/salary-calculator and you are encouraged to explore other 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.
(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 one of your scenarios, 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.
