Applied mathematics and modelling · Maths EE idea · Accessible

The mathematics of a mortgage

A research question to start from

How is the monthly repayment of a loan derived, and how sensitive is the total repaid to the interest rate and term?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

A recurrence relation solved exactly, with sensitivity analysis for discussion.

Mathematics you would need

Recurrence relations
Geometric series
Compound interest
Rates of change

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Derive the repayment formula.
Analyse sensitivity with derivatives or tables.
Discuss assumptions (fixed rates, compounding).

Scope and difficulty

Accessible. Accessible; keep financial advice out.

Pitfalls

Spreadsheet only.
No derivation.

Where to start reading

Search a library catalogue or a university's open lecture notes for: loan amortisation formula derivation geometric series. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

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