Is a longer mortgage ever the better deal?

AI SLAI HLAA SLAA HL Accessible Also in: Pure maths

Research question

For a typical first-time buyer in [my country], how do monthly payments and total interest compare for 25- and 35-year mortgages, and how do overpayments change the comparison?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Longer mortgages are increasingly common because they lower monthly payments, at the cost of much more interest. Deriving the repayment formula from a geometric series and testing strategies makes the maths yours.

The mathematics you'll need

Deriving the annuity/repayment formula from a geometric series
Amortisation tables
Effect of overpayments (recurrence relation)
Interest-rate sensitivity

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use average first-time-buyer prices and current mortgage rates from official statistics (cite the date).

HM Land Registry Price Paid Data — Every residential sale in England and Wales since 1995 (Open Government Licence).
Office for National Statistics (UK) — UK population, earnings, inflation, births and deaths time series.
FRED (Federal Reserve Bank of St. Louis) — 800,000+ economic time series (interest rates, inflation, unemployment) with CSV download.
ECB Data Portal — exchange rates — Daily euro reference rates for 29 currencies and ECB interest rates.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Derive the monthly payment formula.
Compare the two terms.
Model regular overpayments on the longer term.
Vary the interest rate.
Reflect on inflation, flexibility and rate changes during the term.

Pitfalls that cost marks

Using the TVM solver without the formula.
Ignoring that rates are fixed only for a few years.
Unsourced house prices.

Showing personal engagement

Use prices in your own town.
Explain which you would choose and why.
Compare with a family member's experience.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Include a rate change after 5 years and model the new payments.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).