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3.2c · Maths for Personal Finance · Sub-skill
Comparing savings and borrowing rates fairly using AER (for savings) and APR (for loans and credit).
Build it up, step by step
Click each step below to reveal it — work through them in order the first time round.
Banks can quote interest in confusing ways — monthly rates, rates with fees, rates compounded at different frequencies. AER and APR exist to convert all of these into one standard annual percentage, so you can compare products fairly.
AER is used for savings accounts. It shows what the interest rate would be if it were paid once a year, taking into account how often interest actually compounds (e.g. monthly). A higher AER means your savings grow faster.
APR is used for loans, credit cards and mortgages. It represents the total cost of borrowing over a year as a percentage, including interest and most fees/charges. A lower APR means borrowing is cheaper.
When comparing two savings accounts, choose the higher AER (more interest for you). When comparing two loans, choose the lower APR (less cost to you). You can also use the AER/APR directly as a compound interest rate in the multiplier formula $\left(1+\frac{r}{100}\right)^t$ to estimate growth or cost over several years.
Bank A offers a savings account with AER 2.4%. Bank B offers a savings account paying 0.2% interest per month. Which account grows a £1,000 deposit to a larger amount after 1 year?
Bank A: 1000×1.024 = £1,024.00
Bank B: 1000×(1.002)12 ≈ 1000×1.02426 ≈ £1,024.26
Bank B grows the deposit to a slightly larger amount after 1 year, even though its headline monthly rate looked smaller — this is exactly why comparing AER (not just the monthly rate) matters.
Test yourself
A credit card advertises an APR of 22.9%. James borrows £800 on the card and pays none of it back for exactly 1 year.
(a) Calculate how much interest James would owe after 1 year, assuming the APR acts as a simple annual rate for this calculation.
(b) Explain why comparing APR is more useful than just comparing a card's monthly interest rate when choosing a credit card. [4 marks]
(a) Interest = 800 × 0.229 = £183.20.
(b) APR already accounts for how often interest compounds over a year and typically includes fees, converting everything into one standard yearly percentage — so it allows a fair, like-for-like comparison between cards, whereas comparing monthly rates alone could be misleading if cards compound interest differently or have different fees.
Practice
Five short questions on aer/apr. Work through them, then reveal the mark scheme to check.