How the result is calculated
An interest rate tells you what a lender charges on the money you owe. It does not tell you what the loan costs, because most loans carry fees as well: an arrangement fee taken out of the advance, a fee added to the balance, an account charge with every payment. The annual percentage rate folds all of them into one yearly figure, so loans with different mixes of rate and fees can be compared on one number.
Every legal APR in the countries this calculator covers starts from the same idea. Take the money the borrower actually receives and the instalments they pay, fees included, and find the rate at which the instalments, discounted back to the start, add up to exactly what was received.
AΣ P ÷ (1 + i)k, for k = 1 to n
- A
- what the borrower receives: the loan less any fee paid at the start
- P
- each monthly instalment, any monthly fee included
- i
- the monthly rate that makes the two sides equal
- n
- the number of instalments
Where the countries part company is in what they do next. The United States (Regulation Z, Appendix J), Australia (the comparison rate), India (the Key Facts Statement) and Japan multiply the monthly rate by twelve: a nominal rate, with no compounding. Britain (FCA CONC App 1) and every EU country (the Consumer Credit Directive, Annex I, through each national law) time each payment in years and solve for the annual rate directly, which for monthly payments is (1 + i)^12 − 1: an effective rate. Canada's federal regulation uses a different formula altogether, the cost of borrowing divided by the term in years and by the average principal outstanding. New Zealand and Sri Lanka require the interest rate and the fees to be disclosed separately, with no single fee-inclusive rate.
The laws also say how precisely to state the result: two decimals in the United States and Germany, at least one in Britain and the rest of the EU, at least one in Japan.
Worked example
| Item | Amount | How it is obtained |
|---|---|---|
| Monthly instalment | $322.67 | 10,000 at 10% ÷ 12 over 36 months |
| Received, A | $9,700.00 | 10,000 − 300 fee |
| Monthly rate, i | 1.00883% | the rate at which 36 × 322.67 discounts to 9,700 |
| APR | 12.11% | 12 × 1.00883%, to two decimals |
| Cost of credit | $1,916.12 | 36 × 322.67 − 9,700 |
The same loan under the British and European method is 12.8%, and under Canada's formula 11.86%. The loan costs exactly the same in each case; only the measuring stick changes.
| Item | Amount | How it is obtained |
|---|---|---|
| Instalment | 969.73 | 20,000 at 15% ÷ 12 over 24 months |
| Net disbursed | 19,600.00 | 20,000 − 400 |
| Monthly rate | 1.42252% | the IRR of 24 × 969.73 against 19,600 |
| APR | 17.07% | 12 × 1.42252%, as the Key Facts Statement shows |
Reading the result
The headline is the APR the law in your chosen country would require a lender to show, stated to that law's precision and under that law's name: APR, APRC, TAEG, effektiver Jahreszins. Where a country has no fee-inclusive rate, the headline is the nominal yearly cost with the effective figure beside it, labelled as information rather than a legal rate.
The tiles show the monthly instalment, the cost of credit (everything you repay less what you received) and the amount you actually receive. The table runs the same loan through all three methods, which is the honest way to compare a rate quoted in one country with a rate quoted in another.
What changes the result
Fees paid at the start matter most on short loans. A 300 fee on a one-year loan is spread over twelve payments and lifts the APR by several points; on a five-year loan the same fee lifts it by much less. That is why lenders with high upfront fees prefer to advertise long terms.
A fee added to the loan costs a little more than the same fee paid at the start, because you pay interest on it. A monthly account fee raises every instalment, and over a long term it can add more than an upfront fee does.
The method changes the figure but not the cost. The effective method always gives a higher number than the nominal one for the same loan, and the gap widens as rates rise: at a 1% monthly rate it is 12% against 12.68%.
What is not included
The first instalment is assumed to fall one month after the loan is paid out. Regulation Z and the European formula both allow for an odd first period, which moves the APR slightly. Optional insurance, late-payment charges and early-repayment charges are left out, as most laws require. A variable rate is held at its starting level for the whole term, which is also what the European formula assumes. Some countries exclude particular fees from the legal APR, such as German notary and land registry fees; leave those out of the fee fields to match.
Using the result
Compare APRs between lenders in the same country, quoted by the same method; it is the one figure that puts a low-rate, high-fee loan and a high-rate, no-fee loan on the same footing. Do not compare an American APR with a British one directly: convert one to the other's method using the table. And look at the cost of credit in money as well as the APR, because a longer loan can have a lower APR and still cost more in total.