Methods for charging interest

APR is the principal means of comparing credit products. Because interest is compounded on a monthly basis, to calculate charges on a credit card account the APR has to be de-compounded. Most major banks use the following methodology:

Increase the figure to the highest possible value while still meeting advertising requirements. e.g., if a card is advertised at a percentage rate of 17.9, then any value up to 17.949 will still be rounded down to 17.9, and thus still be correct. Once this number has been derived, it must be converted to a decimal multiplier – in this case the number would be 1.17949. To derive the monthly rate, obtain the twelfth root (i.e., raise to the power 1/12). This will provide you with a rate which, when compounded over a year, will equal the APR.

At this point, it is important to round down – because the APR has already been maximised in order to make use of the highest rate possible, rounding any figures up might push the APR over the edge and onto a higher rate, leaving the card issuer liable for false advertising claims.

This method is subject to change, depending on the bank in question, and is highly influenced by cardholder perceptions and bank strategy, sometimes with a value of simplicity for cardholders; other times with the effect of obfuscating the true interest rates charged.

Methods vary by country because of customs and laws. A brief summary of each of the four methods given under U.S. Regulation Z follows, this list followed by a few examples from other countries and some discussion of differences between the various methods:

Average daily balance

The sum of the daily outstanding balances is divided by the number of days covered in the cycle to give an average balance for that period. This amount is multiplied by a constant factor to give an interest charge. The resultant interest is the same as if interest was charged at the close of each day, except that it only compounds (gets added to the principal) once per month. It is the simplest of the four methods in the sense that it produces an interest rate approximating if not exactly equal the expected rate.

Adjusted balance

The balance at the end of the billing cycle is multiplied by a factor in order to give the interest charge. This can result in an actual interest rate lower or higher than the expected one, since it does not take into account the average daily balance, that is, the time value of money actually lent by the bank. It does, however, take into account money that is left lent out over several months.

Previous balance

The reverse happens: the balance at the start of the previous billing cycle is multiplied by the interest factor in order to derive the charge. As with the Adjusted Balance method, this method can result in an interest rate higher or lower than the expected one, but the part of the balance that carries over more than two full cycles is charged at the expected rate.

Two-cycle average daily balance

The sum of the daily balances of the previous two cycles is used, but interest is charged on that amount only over the current cycle. This can result in an actual interest charge that applies the advertised rate to an amount that does not represent the actual amount of money borrowed over time, much different that the expected interest charge. The interest charged on the actual money borrowed over time can vary radically from month-to-month (rather than the APR remaining steady). For example, a cardholder with an average daily balance for the June, July, and August cycles of $100, 1000, 100, will have interest calculated on 550 for July, which is only 55% of the expected interest on 1000, and will have interest calculated on 550 again in August, which is 550% higher than the expected interest on the money actually borrowed over that month, which is 100.

However, when analyzed, the interest on the balance that stays borrowed over the whole time period ($100 in this case) actually does approximate the expected interest rate, just like the other methods, so the variability is only on the balance that varies month-to-month. Therefore, the key to keeping the interest rate stable and close to the "expected rate" (as given by average daily balance method) is to keep the balance close to the same every month. The strategic consumer who has this type of account either pays it all off each month, or makes most charges towards the end of the cycle and payments at the beginning of the cycle to avoid paying too much interest above the expected interest given the interest rate; whereas business cardholders have more sophisticated ways of analyzing and using this type of account for peak cash-flow needs, and willingly pay the "extra" interest to do better business.

Much confusion is caused by and much mis-information given about this method of calculating interest. Because of its complexity for consumers, advisors from Motley Fool (2005) to Credit Advisors (2005) advise consumers to be very wary of this method (unless they can analyze it and achieve true value from it). Despite the confusion of variable interest rates, the bank using this method does have a rationale; that is it costs the bank in strategic opportunity costs to vary the amount loaned from month-to-month, because they have to adjust assets to find the money to loan when it is suddenly borrowed, and find something to do with the money when it is paid back. In that sense, the two-cycle average daily balance can be likened to electric charges for industrial clients, in which the charge is based upon the peak usage rather than the actual usage. And, in fact, this method of charging interest is often used for business cardholders as stated above. These accounts often have much higher credit limits than typically consumer accounts (perhaps tens or hundreds of thousands instead of just thousands).

United Kingdom

The daily accrual method is commonly used in the UK. The annual rate is divided by 365 to give a daily rate. Each day, the balance of the account is multiplied by this rate, and at the end of the cycle the total interest accrued is billed to the account. The effect of this method is theoretically mathematically the same over one year as the average daily balance method, because the interest is compounded monthly, but calculated on daily balances. Although a detailed analysis can be done that shows that the effective interest can be slightly lower or higher each month than with the average daily balance method, depending upon the detailed calculation procedure used and the number of days in each month, the effect over the entire year provides only a trivial opportunity for arbitrage.