Annual Percentage Rate (APR)

Annual percentage rate (APR)
Teacher guidance
Overview of task
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: Finance, Algebra
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
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
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