Understanding annual rates; e.g. AER and APR
GCSE Mathematics – Numeracy and GCSE Mathematics
Solving numerical problems
 Carrying out calculations relating to enterprise, saving and borrowing, investing, appreciation and
depreciation and understanding annual rates, e.g. AER, APR
Possible learning objectives
 Explore the meaning of interest rates
 Carry out calculations relating to saving
 Carry out calculations relating to borrowing
GCSE Mathematics
Possible learning outcomes
 Understand the structure for carrying out a compound interest calculation
 Understand the concept of APR
 Understand the concept of AER
 Calculate the AER in a given situation
 Calculate the APR in a given situation
 Use the AER to carry out calculations in a given situation
 Use the APR to carry out calculations in a given situation
 Use AER to make comparisons between different deals
 Use APR to make comparisons between different deals
Prerequisites
Mathematical language
Pedagogical notes
Interest, simple interest, compound interest
 Convert between fractions, decimals and percentages
 All students are expected to ‘carry out calculations relating to enterprise,
Per annum
saving and borrowing, investing, appreciation and depreciation’. Intermediate
 Round to a given number of decimal places or significant
Loan
tier students should understand compound interest, but only higher tier
figures
Mortgage
students are expected to calculate with annual rates such as AER and APR.
 Find a percentage of an amount using a multiplier
Rate,
fixed
rate,
variable
rate
 ‘Annual percentage rate’ (APR) should only refer to borrowing money, as it is
 Understand the concepts of simple interest and compound
Fixed
the official rate for borrowing. Its purpose is to provide one percentage rate
interest.
Term (of a loan)
that takes account of any fees and allows consumers to compare deals that
Representative
example
they are being offered.
Note two Hwb questions that may be suitable. Both introduce
Appreciate,
appreciation
 ‘Annual equivalent rate’ (AER) – sometimes referred to as EAR instead - should
compound interest, but do not refer to AER. These are suitable for
Depreciate,
depreciation
only refer to saving money, as it is the official rate for saving. It serves the
Intermediate tier.
Annual
Percentage
Rate
same purpose as the APR for borrowing, allowing comparisons to be made
Hwb: Question 14: Comparing interest.
Annual
Equivalent
Rate
between different deals offering interest payable at varying frequencies.
Hwb: Question 15: Double your money.
 The following is an extract from the formula list provided to students:
Notation
Annual Equivalent Rate (AER)
n
APR for Annual Percentage Rate
AER, as a decimal, is calculated using the formula (1 + ni ) − 1, where i is the
AER for Annual Equivalent Rate
nominal interest rate per annum as a decimal and n is the number of
p.a. for per annum
compounding periods per annum.
The ‘%’ symbol
WJEC: New content guidance includes worked examination questions and
annotated candidates’ responses.
See this guide on moneysavingexpert.com for further information.
Reasoning opportunities and probing questions
Possible activities
Potential misconceptions
Hwb: Question 55: Helping to Buy a Home. Focuses on AER
 What is the same and what is different: APR and AER?
 Some students may think that APR and AER serve the same purpose
(using
a
savings
account
to
save
for
a
deposit
on
a
house).
 Convince me that a savings deal offering 4% p.a. payable four
 Some students may think that, for example, 292% p.a. (fixed) is referring to the
Hwb: Question 66: Too good to be true. This focuses on AER.
times a year is better than a deal offering 4% AER
same concept as a fixed rate deal when arranging a mortgage
Hwb:
Question
83:
Quarterly
or
monthly?
A
question
on
AER
that
 Always / Sometimes / Never: An AER is greater than the
 Some students may think that an interest rate of 6% p.a. payable 4 times a year
explores the impact on savings when the interest rate is applied
advertised interest rate.
is the same as an AER of 6% (The AER is actually (1.015)4 – 1 = 6.136% to
over
different
periods.
three decimal places)
 Haydn is offered a loan with an interest rate of 8% p.a. There
Hwb: Task 12: ‘The Arts in Wales’. Focuses on APR, including
are no fees for the loan, and the APR is advertised as 8.24%.
 Some students may not convert a given AER percentage rate into a decimal
loans of 0% from the Arts Council of Wales, to bank loans and
𝑖 𝑛
How many times a year must he make repayments?
before substituting into the compound interest structure of (1 + 𝑛) − 1, or
using a credit card.
they may omit to convert this decimal back into a percentage at the end of a
Hwb: Task 30: Borrowing Money - APR. Note that this could be
multi-step problem
used as an introduction to the concept of APR with higher tier
 Some students may round incorrectly, or they may round early within a multistudents as it only considers cases that involve a single
step problem and present a result based on a compounded error
repayment.