IA idea · Finance & economics
Should I lease or buy my first car?
Research question
Over four years, is leasing, buying with a loan, or buying a used car with savings the cheapest way to have a car, once depreciation, interest and the opportunity cost of savings are included — and how sensitive is the answer to the interest rate?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
It is a decision many students face soon after the IB, and the adverts make it deliberately hard to compare. Financial mathematics — loans, depreciation, compound interest — gives a clear, personal answer and a sensitivity analysis that shows when the answer changes.
The mathematics you'll need
- Loan amortisation and monthly repayments (TVM solver — explain the formula)
- Exponential depreciation fitted to used-car prices
- Compound interest and opportunity cost
- Break-even analysis and sensitivity to interest rate
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
Collect real quotes for one car model (lease, loan) and 30+ used listings of the same model at different ages to fit depreciation.
- ECB Data Portal — exchange rates — Daily euro reference rates for 29 currencies and ECB interest rates.
- FRED (Federal Reserve Bank of St. Louis) — 800,000+ economic time series (interest rates, inflation, unemployment) with CSV download.
- Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.
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
- Define the three options and a fair comparison (same car, same period).
- Fit a depreciation model to used-car prices.
- Compute total cost of each option, including what the car is worth at the end.
- Vary interest rates and mileage to find where the best option changes.
- Reflect on risk, flexibility and what the model leaves out (insurance, repairs).
Pitfalls that cost marks
- Comparing monthly payments rather than total cost.
- Forgetting the car's value at the end of the period.
- Quoting rates with no date or source.
Showing personal engagement
- Use the car you actually want and real local quotes.
- Interview a family member about their car decision.
- State the interest rate at which you would change your mind.
See Criterion C: personal engagement for what examiners look for.
Taking it further
HL: fit the depreciation with a logarithmic transformation and a confidence band, and use it to find the age at which buying used is cheapest per year of ownership.
See it done
Our annotated exemplar Should I lease or buy my first car? (AI SL) explores a question like this one, with an examiner's comment on every criterion.