Finance⏱ 5 min read
How APR Is Calculated — and Why It Can Still Mislead You
APR standardises loan comparison, but the calculation method means two loans with identical APR can have very different true costs. Here is the maths behind APR and its key limitation.
APR (Annual Percentage Rate) is the single most important number when comparing loans — but it has a well-known limitation that most borrowers don't know about. Understanding the calculation makes you a far better consumer of credit.
How APR Is Calculated
APR is the discount rate that makes the present value of all
future payments equal to the amount borrowed (net of fees).
It's an internal rate of return (IRR) calculation applied to loans.
Simple example: £10,000 borrowed, repaid as £12,000 in one year
APR = (12,000/10,000)^(1/1) - 1 = 20% APR
With monthly compounding (more realistic):
The same £12,000 repaid monthly over 12 months:
Each monthly payment: £12,000/12 = £1,000
APR is the annual rate r where:
10,000 = 1000/(1+r/12) + 1000/(1+r/12)^2 + ... + 1000/(1+r/12)^12
Solving: r ≈ 35.1% APR
(The same total repayment looks much worse as APR when monthly)
APR Including Fees
UK law requires APR to include all mandatory charges.
This makes it better than just the interest rate for comparison.
Example: £5,000 loan, 2-year term
Interest rate: 8% per year
Arrangement fee: £200 (added to loan at start)
Without fee: APR ≈ 8%
With £200 fee added to loan:
Effective amount borrowed: £5,200
Monthly payment: approximately £235
True APR ≈ 12.3% (fee significantly raises APR on small loan)
This is why arrangement fees matter more on smaller, shorter loans.
The same £200 fee on a £100,000 mortgage over 25 years barely
moves the APR.
The Key Limitation: Timing Assumptions
APR assumes you keep the loan for its full term.
This can make longer-term loans look cheaper than they are.
Example: Two credit cards, £1,000 balance
Card A: 20% APR, no annual fee
Card B: 18% APR, £50 annual fee
If you pay off in 6 months:
Card A total cost: ~£51 interest
Card B total cost: ~£45 interest + £25 pro-rata fee = ~£70
Card A is cheaper despite higher APR.
APR only tells you the cheapest option if you hold
for exactly the assumed term. For products you'll pay off early,
compare total cost directly, not just APR.
Representative APR
Lenders must offer the advertised APR to at least 51% of
applicants who are accepted.
The remaining 49% can receive a higher rate.
"Representative APR" is therefore a minimum for most people,
not a guaranteed rate.
If you have an imperfect credit history:
Your actual APR may be 1.5-3x the representative APR.
Always check the actual rate offered to you before accepting —
the representative figure in the advertisement is not a promise.
Effective Annual Rate vs APR
EAR = (1 + APR/n)^n - 1
(where n = compounding periods per year)
For a 20% APR compounded monthly:
EAR = (1 + 0.20/12)^12 - 1 = (1.01667)^12 - 1 = 21.94%
The EAR is always higher than or equal to APR.
For savings: AER (Annual Equivalent Rate) = same concept.
EAR/AER is the true annual rate — APR understates the cost
for monthly-compounding products.