GCSEMathsWJECMaths & Numeracy (Double Award)HigherRevision NotesNumberFinance, Money & InterestAnnual Percentage Rate (APR)

Annual Percentage Rate (APR) (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Exam code: 3320

Jamie Wood

Written by: Jamie Wood

Reviewed by: Mark Curtis

Updated on

Annual Percentage Rate (APR)

What is APR?

  • APR (Annual Percentage Rate) is used to compare different loans or borrowing products across a year

    • It takes into account differences in interest rates, amounts borrowed, repayment intervals, and when interest is charged

    • This is different from AER (Annual Equivalent Rate) which compares the interest rates for savings accounts

  • Different loans, mortgages, and credit cards can have very different terms, fees, and repayment plans

    • This makes it harder to compare them directly to find the best deal

    • APR makes comparisons much easier and fairer

  • In the UK, it is a legal requirement that lenders disclose the APR for a loan before an agreement is made

How do I answer questions involving APR?

  • In exam questions involving APR, any formulas needed will be given in the question

  • They may not ask you to calculate APR directly

    • It is more likely that you will be asked to calculate something else, like monthly payments, using APR

  • For example, you may be given a formula to find the monthly payment on a loan

    • M equals fraction numerator r cross times L over denominator 1 minus open parentheses 1 plus r close parentheses to the power of negative n end exponent end fraction where:

      • M is the amount of each monthly repayment

      • L is the loan needed

      • r is the monthly interest rate as a decimal (this is APR divided by 12)

      • n is the number of months taken to pay back the loan.

  • You need to be confident substituting into a given formula

  • The most important thing is to understand the concept of APR as a figure for comparing borrowing products

  • The formula above can be used to find the monthly payments, and therefore the total amount paid over the full term of the loan

Worked Example

Elis is buying a new motorbike, priced at £15 000. He is going to take out a loan to buy the motorbike.

The table below shows his finance options:

Option A

Option B

Deposit

£1000

£0

Loan amount

£14 000

£15 000

Loan period

3 years

5 years

APR

5.4%

5.4%

Monthly repayment

£285.83

(a) Use the formula below to calculate the monthly payment for Option A.

M equals fraction numerator r cross times L over denominator 1 minus open parentheses 1 plus r close parentheses to the power of negative n end exponent end fraction where:

  • M is the amount of each monthly repayment

  • L is the loan needed

  • r is the monthly interest rate as a decimal (this is APR divided by 12)

  • n is the number of months taken to pay back the loan.

Answer:

L is £14 000 (£1000 has been paid as a deposit)

r is the monthly interest rate, so divide the APR (which is annual) by 12

Remember to write it as a decimal rather than a percentage

r equals 0.054 divided by 12 equals 0.0045

n is the number of months taken to pay back the loan

n equals 3 cross times 12 equals 36

Substitute these into the formula

table row M equals cell fraction numerator r cross times L over denominator 1 minus open parentheses 1 plus r close parentheses to the power of negative n end exponent end fraction end cell row M equals cell fraction numerator 0.0045 cross times 14000 over denominator 1 minus open parentheses 1 plus 0.0045 close parentheses to the power of negative 36 end exponent end fraction end cell end table

Work this out using your calculator

M equals 422.1114569

Round to nearest penny

Monthly payment for Option A = £422.11

(b) Calculate the total amount Elis will pay for each option.

Answer:

Multiply the monthly payment by the number of months it is paid for

Option A: 422.11 cross times open parentheses 12 cross times 3 close parentheses

Total for Option A = £15 195.96

Option B: 285.83 cross times open parentheses 12 cross times 5 close parentheses

Total for Option B = £17 149.80

(c) Suggest a reason why Elis may choose Option A, and a reason why Elis may choose Option B.

Answer:

Option A offers a lower overall cost over the full term of the loan

Option B offers lower monthly payments, which may make budgeting easier

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Mark Curtis

    Reviewer: Mark Curtis

    Expertise: Maths Content Creator

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.