Turn a flat rate
into an APR
To convert a flat rate to an APR, work out the monthly payment the flat rate produces, find the reducing-balance rate that gives the same payment, then compound it over a year. On a monthly loan of one to five years the APR usually comes out at between 1.8 and 2 times the flat rate. The calculator below does the sum exactly.
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Convert a flat rate
Set the flat rate you were quoted, the term and the amount. The APR is the annual rate on the reducing balance that gives exactly the same monthly payment.
Before fees. An arrangement or documentation fee pushes the real APR higher than this, and a lender’s own APR should include any compulsory charge. The calculation runs in your browser and nothing you enter is sent anywhere.
The method, in four steps
1. Work out the flat interest. Multiply the amount by the flat rate and by the number of years. That is the whole interest bill, fixed on day one, because a flat rate is charged on the original sum regardless of how much you have paid back.
2. Work out the monthly payment. Add the interest to the amount and divide by the number of monthly payments.
3. Find the reducing-balance rate. Ask what monthly rate, charged only on the balance still owed, would produce that same payment. There is no tidy formula for this step, so it is found by trial: try a rate, see whether the payment comes out too high or too low, and narrow it down. A spreadsheet does it instantly with =RATE(months, -payment, amount).
4. Turn the monthly rate into an annual one. Add one, raise it to the power of twelve and take one away. Multiplying by twelve instead gives a slightly lower nominal figure; the compounded version is how an APR is stated in the UK.
£30,000 at 6% flat over three years
The four steps on one quote. These are the figures the calculator opens on.
Before fees. Put the same loan through at 11.7% APR on any loan calculator and you get the same £983 a month, which is the check that the conversion is right.
Why the answer is nearly double
Over a loan repaid in equal instalments, you hold on average only a little over half the money you borrowed: all of it in the first month, almost none of it in the last. A flat rate charges you as if you held all of it throughout. Spread the same interest over roughly half the borrowing and the true rate comes out at roughly twice the flat one.
It is not exactly double, and the gap moves with the term. On the usual one-to-three-year loans the multiple sits close to 1.9 to 2. On very short loans it is lower, because there is little time for the balance to fall, and on long ones it drifts down again because compounding works the other way. At 6% flat, six months comes out at about 10.7% APR, three years at 11.7% and seven years at 11.1%.
There is also a pencil shortcut, sometimes taught as the N-ratio method: multiply the flat rate by twice the number of payments and divide by the number of payments plus one. For 6% over 36 payments that gives 11.7%, almost exactly right. It holds up well around three years and at ordinary rates, and overstates on long terms or high rates, so use the calculator when the answer matters.
What this converter leaves out
Fees, first. A lender’s own APR should include any compulsory arrangement or documentation fee, so a quote with a fee will show a higher APR than this page does. If the fee is added to the loan rather than paid up front, you are also paying the flat rate on the fee.
Second, irregular schedules. A balloon payment at the end, a deposit, seasonal payments or weekly collections all change the answer, and the arithmetic above assumes equal monthly payments starting a month after the money arrives. For anything unusual, ask for the APR in writing and for the total amount repayable, and compare the totals. For the reasoning behind all of this, read flat rate vs APR.
Got a flat rate quote? Send it to us and we will set it beside our options in the same units.
Get my optionsCommon questions
Is there a formula to convert a flat rate to an APR?
Not an exact one you can write on a single line, because the middle step has to be solved by trial. The close shortcut is flat rate × 2n ÷ (n + 1), where n is the number of monthly payments. It is accurate to a few tenths of a point on three-year loans and drifts on long terms, which is why the calculator above solves it properly.
What is the spreadsheet formula for turning a flat rate into an APR?
Work out the monthly payment first, then use RATE. For £30,000 at 6% flat over 36 months the payment is £983.33, so =RATE(36,-983.33,30000) returns the monthly rate, about 0.92%. Then =(1+that)^12-1 gives the APR, about 11.7%.
Does a longer term make the APR higher for the same flat rate?
Less than you would expect. The multiple peaks around one to three years and eases on longer loans, so 6% flat is about 11.5% APR over a year and 11.1% over seven. What a longer term does raise sharply is the total interest, because a flat rate charges the full amount for every year.
Is a flat rate the same as an add-on rate?
Yes, in practice. Both mean the interest is calculated once on the original amount and added on top, then the total is split into equal payments. You will meet the term on asset finance and older hire purchase quotes as well as some business loans.
Can I use this for a weekly or daily repayment loan?
Only as a rough guide. More frequent payments pay the balance down faster, so the true APR on a weekly-repaid loan is slightly higher than the monthly figure shown here. Ask the lender for the APR and the total repayable and compare those.
Compare the totals, not the rates
Our enquiry shows every option with its monthly payment, total repaid and interest in pounds.
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