Annual Equivalent Rate (AER) (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Annual Equivalent Rate (AER)

What is AER?

• AER (Annual Equivalent Rate) is used to compare different savings accounts across a year

  • It takes into account differences in interest rate and how often interest is paid

  • This is different from APR (Annual Percentage Rate) which compares the interest rates for borrowing money

• Different savings accounts will pay interest at different intervals

  • This is usually either annually or monthly

• Earning 12% interest, only paid at the end of 1 year, will result in a different final balance to earning 1% interest each month, paid monthly (12 times per year)

  • Consider a balance of £100 paid 12% at the end of 1 year

    • £100 × 1.12¹ = £112

    • This is an Annual Equivalent Rate of 12%

  • Consider the same balance subject to 1% interest, 12 times through the year

    • £100 × 1.01¹² = £112.68

    • This is an Annual Equivalent Rate of 12.68%

• AER is used so that the different interest rates and payment intervals can be incorporated into a single figure for easier comparison

How do I calculate AER?

• The formula for AER is given on the formula sheet at the front of your exam paper; it is written exactly as below:

  • AER as a decimal, is calculated using the formula , where is the nominal interest rate per annum as a decimal and is the number of compounding periods per annum

• A nominal interest rate is the annual rate of interest without considering any compounding of the interest

• Be careful with and , read the question carefully

  • is the nominal interest rate per annum

  • A bank may offer 3% interest annually, paid monthly

    • This means and

  • A bank may offer 0.4% interest per month, paid monthly

    • The annual nominal interest rate will be 12 times the monthly nominal interest rate

    • and