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?

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

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

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 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.

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 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.

Taking it further

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

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).