APPM 2360 • Differential Equations • Modeling
Differential Equations: Mortgage Analysis Project
An in-depth look at the project, process, and report.
This project analyzed fixed-rate and adjustable-rate mortgages using differential equation models to compare interest rates and find the most advantageous combination of mortgage type, time, and down payment in order to minimize the total amount paid.
Overview
Our goal was to create models using our learnings from the differential equations section of the class and use those models to compare different mortgage structures, including fixed-rate and adjustable-rate options. We utilized a walkthrough method where we presented all the options, using figures to clarify the long-term behavior of the loans, before presenting our conclusions. We provided a full mathematical breakdown in an appendix in order to improve the readability of the report to a non-technical audience.
What We Did
We derived and analyzed differential equation models describing mortgage balances over time. We then compared scenarios with different rates, loan lengths, and down payments.
Tools Used
- Differential Equation Models
- Matlab
- LaTeX
- Technical writing
What I Learned
This project taught me how to apply what I learn in the classroom in a tangible manner. Oftentimes when studying math I find myself pondering how I will use a certain concept in my career, and application is usually glanced over in the classroom. However, we learn the curriculum in school because it is valuable to know those concepts, even though it might not be readily apparent how they might be used. I learned that the abstract concepts that I wrestled with throughout the first weeks of the class can be applied to at least one field outside of the theoretical frame in which they were presented. Furthermore, this project taught me how to take concepts that I learn, and gave me an example of how I might leverage that knowledge in order to advance my understanding and proficiency as an engineer.