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UK Student Loans: A Tax on the Poor?

Mathematical Modeling

UK student loans are said to cost the poor more than the rich because lower earners repay for longer. Build a financial model to investigate whether this claim holds up.

Introduction

In the UK student loan system, graduates repay 9% of earnings above a threshold. Higher earners clear their debt faster, while lower earners may repay for the full 30-year term before the balance is written off — often having paid more in total due to accumulated interest. Critics argue this makes the system regressive: effectively a 30-year tax on lower-income graduates. This exploration asks students to build financial models comparing total repayment across different salary trajectories. It connects percentage calculations, compound interest, sequences and series, and statistical modelling to a live political and economic debate.

Guiding Questions
  • How much does a graduate earning £30,000 repay per year? What about one earning £60,000?
  • How does compound interest affect the total amount repaid at different salary levels?
  • At what salary level does a graduate clear their loan before the 30-year write-off?
  • Is it accurate to call this system 'regressive'? What does your model show?
  • How sensitive is your model to assumptions about salary growth and interest rates?
Key Mathematical Concepts
Statistics Compound Interest Financial Mathematics Modelling Sequences and Series
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