Mathematical Modelling and Analysis of Mortgage-Style Loan Repayment

Overview:
This project explores the mathematical modeling of mortgage-style loan repayment using concepts from financial mathematics and amortization theory. It provides a framework for understanding how loans are repaid over time, with detailed step-by-step calculations of monthly interest, principal repayment, cumulative totals, and remaining balances. The project emphasizes the role of amortization schedules and fixed monthly payment formulas in analyzing long-term debt repayment. By bridging theoretical models and practical tables, it equips students with the ability to interpret financial dynamics such as decreasing interest burden, increasing principal contributions, and the effect of extra payments.

Suitable For:

• BS Mathematics – applied financial mathematics, discrete modeling, step-by-step amortization

• BS Statistics – cumulative calculations, tabular analysis, and repayment visualization

• BS Computer Science – algorithmic implementation of amortization schedules

• BS Finance/Commerce – cumulative calculations   of amortization schedules

Technologies Used:

• Programming Language: Python (for automation of repayment calculations)

• Libraries & Tools: NumPy, Pandas, Matplotlib, LaTeX for documentation

• Techniques: Fixed payment formula, monthly interest computation, amortization schedules, cumulative totals

• Visualization: Loan repayment tables, cumulative interest vs. principal charts

Features:

• Development of a mathematical model for loan repayment with precise formulas

• Step-by-step demonstration of interest, principal, and balance updates over time

• Worked examples with real-world values (e.g., $250,000 loan at 6.5% annual interest for 30 years)

• Comprehensive amortization tables showing monthly breakdowns

• Analysis of cumulative interest and principal with financial interpretation

• Flexibility to incorporate extra payments and study their impact on loan duration

Deliverables:

• Complete Python source code for amortization schedule automation

• Project documentation: setup guide, formulas, methodology, and detailed worked examples

• Presentation slides (PPT): objectives, formulas, worked examples, and results tables/figures

• Visual assets: repayment tables and cumulative interest–principal graphs

Support:

• Guidance for understanding, modifying, or extending the repayment model to new scenarios (different loan sizes, rates, or extra payments)

Benefits for Students:

• Gain hands-on experience in financial mathematics and amortization theory

• Understand the mathematics behind fixed loan repayment and cumulative interest

• Learn to compute repayment tables both manually and programmatically

• Strengthen skills in data visualization and financial interpretation

• Excellent capstone choice for demonstrating applied mathematics, finance, and computational modeling