From nominal rate to APR
The nominal rate is what they advertise; the APR is what compares. Here is the real APR, with the arrangement fee spread across the life of the loan.
Your figures
Result
- APR from compounding alone
- 3.042%
- Monthly payment
- $632.41
- Arrangement fee
- $1,500.00
- Total cost of the loan
- $79,166.18
Where each point of the gap comes from
| Item | Annual rate |
|---|---|
| Nominal rate the lender quotes | 3.000% |
| Effective rate from compounding alone | 3.042% |
| Real effective rate, fees included | 3.123% |
What we assume
- The loan has level payments (amortising) at a fixed rate.
- The nominal rate is divided by 12 to get the monthly rate, as lenders apply it.
- Only the arrangement fee is included: no valuation, legal fees or insurance.
- A real offer’s APR can be higher if it requires tied products.
How it is calculated
The nominal rate and the APR measure different things, which is why they never match.
The nominal rate is exactly that: divide it by twelve to get the monthly rate and its job is done. It is the big number in the window.
The APR answers a different question: if this deal were a single annual deposit, what rate would it have to be to cost the same? So it includes two things the nominal rate ignores.
First step: compounding
Paying twelve times a year is not the same as paying once:
APR = (1 + nominal / 12)^12 − 1
A 3% nominal rate gives an APR of 3.042% with not a single fee involved. Four hundredths appear on their own, purely from frequency.
Second step: the fees
Here there is no closed formula. The arrangement fee is paid in full on day one, so you receive less than you repay as if you had received the whole thing. The APR is the rate that balances those real flows - what comes in against what goes out - and it is found by approximation.
On £150,000 at 3% over 30 years with a 1% fee, the APR rises to 3.123%.
Why the term changes what the fee does
Because that £1,500 gets spread across every month. On a 30-year loan it weighs eight hundredths; on the same loan over 5 years, more than forty. The same fee hurts five times more on a short term, which is exactly the opposite of how it looks.
Hence a practical rule: on short loans, look at the fee before the rate.
Why APR exists
So that things can be compared. The law requires it precisely because two offers with the same nominal rate and different fees do not cost the same, and without a common figure there would be no way to tell. When choosing between two loans, the APR is what decides.
An example
A mortgage of £150,000 at 3% nominal over 30 years with a 1% arrangement fee has a payment of £632.41 and an APR of 3.123%. Without the fee it would be 3.042%: four hundredths from compounding and eight more from the fee.
Frequently asked questions
Why is my lender’s APR higher than this?
Because the official APR includes every compulsory cost: valuation, tied insurance, arrangement and study fees. Only the arrangement fee goes in here, so this figure is a floor. If the loan requires life cover, the real APR climbs considerably.
Can you go from APR back to the nominal rate?
Without fees, yes: nominal = ((1 + APR)^(1/12) − 1) × 12. With fees there is no clean way back, because the APR mixes the rate with costs that depend on the term and the amount.
Does it work for variable-rate mortgages?
Only as a snapshot. On a variable mortgage the rate changes at every review, so what lenders publish is a "variable APR": a calculation that assumes the index stays exactly where it is today, which it will not.
Does a savings account APR include fees too?
On a deposit the APR works the other way round: it is what you genuinely earn after compounding, and there it usually sits very close to the nominal rate because there are no costs to spread. The difference comes only from how often they pay you.
Keep calculating
All tools →- Loan payment calculator Work out the monthly payment on a loan or mortgage and, above all, how much you will end up paying in interest.
- Loan amortisation schedule Every payment broken down. The interesting part is not the total, it is watching how long it takes before you are mostly paying off the debt.
- Early repayment: term or payment One lump sum, two ways to use it. Which saves more interest is not close, but the other one has its reasons.
- How much mortgage can I afford Two things limit you: what you can pay each month and what you have saved. We tell you which one is binding, because that decides what to do about it.
- Debt-to-income ratio The figure a lender looks at before any other. Not how much you earn, but how much of it is already spoken for.
Updated on 2026-09-11. Calculations run in your browser; nothing you type is sent to a server.