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

How much does it cost to start saving ten years later?

AI SLAI HLAA SLAA HL Accessible Also in: Pure maths

Research question

To reach the same pension pot at 67, how much more per month must someone save if they start at 32 rather than 22, and how does the answer depend on the real rate of return?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Compound growth is most powerful over long periods, which is why starting early matters so much. Quantifying the cost of waiting with future-value annuities is simple mathematics with a life-changing message.

The mathematics you'll need

Future value of an annuity (geometric series)
Real vs nominal returns
Solving for payment given a target
Sensitivity analysis and graphs

Where the data comes from

Use long-run inflation and return figures from central-bank or statistics sources, stating the period used.

FRED (Federal Reserve Bank of St. Louis) — 800,000+ economic time series (interest rates, inflation, unemployment) with CSV download.
Office for National Statistics (UK) — UK population, earnings, inflation, births and deaths time series.
ECB Data Portal — exchange rates — Daily euro reference rates for 29 currencies and ECB interest rates.

Real data for this idea

Primary source: 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 future value of regular payments.
Compute the required monthly saving for each start age.
Compare across real returns of 1–5%.
Add a career break.
Reflect on risk and assumptions about constant returns.

Pitfalls that cost marks

Mixing nominal and real rates.
Presenting investment returns as guaranteed.
No sensitivity analysis.

Showing personal engagement

Use your own planned timeline.
Survey adults about when they started saving.
Design a visual that would persuade a friend.

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	Future value of an annuity (geometric series); Real vs nominal returns
AA HL	Fits, but add an HL technique	Future value of an annuity (geometric series); Real vs nominal returns
AI SL	Good fit	Future value of an annuity (geometric series); Real vs nominal returns
AI HL	Fits, but add an HL technique	Future value of an annuity (geometric series); Real vs nominal returns

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: mixing nominal and real rates; and presenting investment returns as guaranteed. Say how each one affects your answer.

Use of mathematics (E)

SL: future value of an annuity (geometric series); real vs nominal returns; solving for payment given a target; sensitivity analysis and graphs, 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

Model returns as random (simulation with a given mean and standard deviation) and show the spread of outcomes.

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?

Future value of an annuity (geometric series), real vs nominal returns, solving for payment given a target and sensitivity analysis and graphs.

Where can I get data for this IA?

Use long-run inflation and return figures from central-bank or statistics sources, stating the period used. Checked sources and tools: Office for National Statistics (UK), FRED (Federal Reserve Bank of St. Louis) and ECB Data Portal — exchange rates.

Turn this idea into your IA

The planner opens with “How much does it cost to start saving ten years later?” filled in: the question, the maths and the data sources.

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