APR is a standardized expression of the interest rate that applies to a loan or credit card, taking into account at least some of the one-time fees that are applied by the lender. There are several ways to calculate APR, but the process generally includes 3 main steps. Firstly, all one-time costs are added onto the loan amount. Next, the monthly repayment for the loan is calculated based on the loan's specified interest rate. Finally, the interest rate, that would have to be applied to the full loan amount in order for its repayments to equal the calculated monthly repayment, is calculated.

To see this in action, consider the following simplified example where you borrow $1,000 and there is a loan setup fee of $50, making the total amount borrowed $1m050. If the interest rate is 10% (compounding monthly) and the term of the loan is 12 months, then you will need monthly repayments of $92.32 to pay off the $1,050. However, a for the monthly payment of a 12 month, $1,000 loan to be $92.32 would require an interest rate of 19.32%. So, the APR is 19,32%. If the term of the loan was longer, for example the loan was for 10 years instead of 12 months, then the loan fees would be spread across this period, and the APR would drop significantly.

The aim of using APR is to calculate a total cost of borrowing, and to make the interest understandable to an average consumer, so that they can compare loans to determine the best deal and also understand the loans that they already have.

Unfortunately, despite repeated attempts by regulators to establish a single standard for the calculation of APR, it does not always represent the total cost of borrowing nor does it really create a standard that allows consumers to precisely compare the costs of a loan.

The main issues in the calculation of APR arise because the definition for the calculation of APR does not specify which one-time fees must be included and which can be excluded. For example, should APR take into account fees and commissions that are paid to someone other than the lender ? Should APR include penalties, such as late fees ? As a result, it is partly up to the lender to determine which fees are included (or not) in the calculation of APR.

In addition, APR is also highly dependent on the term of the loan. For example, the APR for a loan with a 25 year duration cannot easily be compared to the APR for another loan with a 15 year duration.

For credit cards the APR is a much simpler calculation. Due to the fact that the amount of money borrowed really isn't known, you can not use the formula that is used for most loans. It's simply a calculation of what the effective interest rate is for one year when you take into account that the interest is compounded monthly.

The formula for this is apr=(interest/12 + 1)^12. So for a card with a 10% interest rate it would be apr=(0.1%/12)^12, which is apr=1.0083^12, so apr=1.104 or approximated 11%. Really you should never have to calculate this yourself though.