IA idea · Finance & economics
Contract or SIM-only? The real cost of a new phone
Research question
For a particular phone, is a 24-month contract cheaper than buying the phone outright (or with a loan) plus a SIM-only plan, once resale value and interest are included?
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Why it makes a good exploration
Phone contracts hide the phone's price inside the monthly bill. Separating the two with financial mathematics gives a clear answer about a purchase almost every student makes.
The mathematics you'll need
- Total cost and implied interest rate (TVM)
- Resale value modelled with depreciation
- Break-even analysis
- Linear and piecewise cost functions
Modelling the data, step by step
This idea usually needs a piecewise model. See it worked step by step, with a criterion tip at every step: Piecewise models.
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Where the data comes from
Collect current prices for one phone model from network and retailer websites; resale prices of older models from resale sites.
- Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.
A possible outline
- Define comparable options.
- Compute total cost for each.
- Find the implied interest rate of the contract.
- Include resale value and different usage needs.
- Reflect on price rises during contracts and flexibility.
Pitfalls that cost marks
- Comparing different data allowances.
- Ignoring mid-contract price rises.
- Undated prices.
Showing personal engagement
- Use your own phone and plan.
- Compare with what your family pays.
- Advise a friend with different usage.
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 | Total cost and implied interest rate (TVM); Resale value modelled with depreciation |
| 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 | Total cost and implied interest rate (TVM); Resale value modelled with depreciation |
| AI HL | Not a natural fit | The mathematics is mainly from the AA course; an AI HL version would need modelling with technology, statistics or networks at HL level. |
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: comparing different data allowances; and ignoring mid-contract price rises. Say how each one affects your answer.
Use of mathematics (E)
SL: total cost and implied interest rate (TVM); resale value modelled with depreciation; break-even analysis; linear and piecewise cost functions, 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
Build a general rule: for which phone prices and SIM prices is a contract ever cheaper?
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 and AA SL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.
What mathematics does this IA use?
Total cost and implied interest rate (TVM), resale value modelled with depreciation, break-even analysis and linear and piecewise cost functions.
Where can I get data for this IA?
Collect current prices for one phone model from network and retailer websites; resale prices of older models from resale sites. Checked sources and tools: Desmos graphing calculator.
Turn this idea into your IA
The planner opens with “Contract or SIM-only? The real cost of a new phone” filled in: the question, the maths and the data sources.
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