Nuffield - Annual Percentage Rate (APR)

This introduces APR, the interest charge that is involved when we borrow money, and how to calculate it for both a whole number and a fractional number of year length terms. It also suggests reasons why people want to borrow money.

Mathematical strand

Financial Maths, Algebra and Graphs

Prior knowledge

Previous knowledge of calculating percentages and calculations involving roots (using the indices button and its inverse on a calculator) would be useful.

Relevance to Core Maths qualifications

  • AQA
  • Eduqas
  • Pearson/ Edexcel
  • OCR

Suggested approaches

The task could be used with an investigative approach, where students are given loan amounts, total amount repaid, APR and length of loan – in order to come up with a formula to connect them. Students can then use the formula to calculate the APR in different situations within the worksheet.


In addition to this overview, there are:
• Detailed teacher notes (Word and PDF)
• Student worksheet (Word and PDF)
• PowerPoint presentation

Relevant digital technologies

Access to a calculator or to a spreadsheet is needed. Internet access might also be useful.

Possible extensions

Students could look at examples where more than one payment is made (as is normal with most loans and mortgages) and how this can complicate the calculation.


This is a resource developed by the Nuffield Foundation for the FSMQs and can be accessed at