Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

Make it yours, then agree it with your teacher.

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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

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.

Real data for this idea

Primary source: HM Land Registry Price Paid Data: Price Paid Data. Download one year's file and filter to one town; use price, date and postcode. Licence: Open Government Licence v3.0 (read the address-data note on the page).
Also useful: Office for National Statistics (UK): CPIH annual rate (series L55O). Download the CSV of monthly and yearly 12-month rates. Licence: Open Government Licence v3.0: free to reuse with an acknowledgement.

If you use FRED (listed above), treat it as link-only: download series for your own analysis, but link to them rather than copying FRED's data into anything you publish. Links checked October 2026; we link to the data and never copy it. More free data sets.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Deriving the annuity/repayment formula from a geometric series; Amortisation tables
AA HL	Fits, but add an HL technique	Deriving the annuity/repayment formula from a geometric series; Amortisation tables
AI SL	Good fit	Deriving the annuity/repayment formula from a geometric series; Amortisation tables
AI HL	Fits, but add an HL technique	Deriving the annuity/repayment formula from a geometric series; Amortisation tables

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: using the TVM solver without the formula; and ignoring that rates are fixed only for a few years. Say how each one affects your answer.

Use of mathematics (E)

SL: deriving the annuity/repayment formula from a geometric series; amortisation tables; effect of overpayments (recurrence relation); interest-rate sensitivity, each explained in your own words and carried out correctly.

How finance explorations reach the top bands in general: Finance & economics IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL finance exploration adds.

See a complete IA, marked

Should I lease or buy my first car? (AI SL) is a complete finance exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Deriving the annuity/repayment formula from a geometric series, amortisation tables, effect of overpayments (recurrence relation) and interest-rate sensitivity.

Where can I get data for this IA?

Use average first-time-buyer prices and current mortgage rates from official statistics (cite the date). Checked sources and tools: HM Land Registry Price Paid Data, Office for National Statistics (UK), FRED (Federal Reserve Bank of St. Louis) and ECB Data Portal — exchange rates.

Turn this idea into your IA

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