IA idea · Finance & economics
Will I ever repay my student loan?
Research question
Under the current rules of [my country's student-loan scheme], how does the total amount repaid depend on starting salary and salary growth, and for which careers is the loan effectively a graduate tax?
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Why it makes a good exploration
Income-contingent loans behave strangely: some graduates repay more than they borrowed, others have most of it written off. Modelling it with the published rules gives answers that matter to your own future.
The mathematics you'll need
- Recurrence relations month by month (spreadsheet)
- Compound interest and geometric growth of salary
- Piecewise functions (repayment thresholds)
- Sensitivity analysis
Where the data comes from
Use the official scheme's published interest rate, repayment threshold, rate and write-off period (cite the date); starting salaries by degree from government graduate outcome statistics.
- Office for National Statistics (UK) — UK population, earnings, inflation, births and deaths time series.
- Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.
Real data for this idea
- Primary source: GOV.UK rates and thresholds: Repaying your student loan: what you pay. Take the threshold and rate for your plan type and note the date you read them. Licence: Open Government Licence v3.0.
- 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.
Links checked October 2026; we link to the data and never copy it. More free data sets.
A possible outline
- Summarise the scheme's rules carefully, with sources.
- Build a month-by-month model.
- Run it for several salary paths.
- Find the salary at which total repayments are highest.
- Reflect on rule changes, career breaks and inflation.
Pitfalls that cost marks
- Using out-of-date rules.
- Ignoring inflation when comparing money across 30 years.
- Presenting one scenario as a prediction.
Showing personal engagement
- Model your own intended career path.
- Compare two countries' systems.
- Explain the result to a parent and record their reaction.
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 | Recurrence relations month by month (spreadsheet); Compound interest and geometric growth of salary |
| AA HL | Not a natural fit | The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E. |
| AI SL | Good fit | Recurrence relations month by month (spreadsheet); Compound interest and geometric growth of salary |
| AI HL | Good fit | Recurrence relations month by month (spreadsheet); Compound interest and geometric growth of salary |
Level: Solid. Needs some independent work beyond class examples. 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 out-of-date rules; and ignoring inflation when comparing money across 30 years. Say how each one affects your answer.
Use of mathematics (E)
SL: recurrence relations month by month (spreadsheet); compound interest and geometric growth of salary; piecewise functions (repayment thresholds); sensitivity analysis, 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
Discount future repayments to present value and compare with the amount borrowed.
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 and AA SL. We rate it Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Recurrence relations month by month (spreadsheet), compound interest and geometric growth of salary, piecewise functions (repayment thresholds) and sensitivity analysis.
Where can I get data for this IA?
Use the official scheme's published interest rate, repayment threshold, rate and write-off period (cite the date); starting salaries by degree from government graduate outcome statistics. Checked sources and tools: GOV.UK rates and thresholds, Office for National Statistics (UK) and Desmos graphing calculator.
Turn this idea into your IA
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