Credit card interest

Credit card interest is the principal way in which card issuers generate revenue.

In a typical UK card issuer, between 80% and 90% of cardholder generated income is derived from interest charges. A further 10% is made up from default fees. As a result, optimal calculation of interest is key to a card issuer's profitability.

Calculating a Monthly Rate

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 - since 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. However, given that this method provides the highest returns for a given APR, it is likely that most (if not all) banks use it.

Methods of Charging Interest

In the United States, there are four commonly accepted methods of charging interest. These are detailed in Regulation Z of the Truth in Lending Act. There is a legal obligation on US issuers that the method of charging interest is disclosed and is sufficiently transparent to be fair. This is typically done in the Schumer Box.

That said, there are not just four prescribed ways to charge interest i.e. those specified in Regulation Z. US issuers can charge interest according to any method they choose. The four (or arguably six) "safe-harbour" ways to describe and charge interest are detailed in Regulation Z. If an issuer charges interest in one of these ways then there is a shorthand description of that method in Regulation Z that can be used. If a lender uses that description, and charges interest in that way, then their disclosure is deemed to be sufficiently transparent and fair. If not, then they must provide an explanation of the method used.

Because of the safe-harbour definitions, US lenders have tended to gravitate towards these methods of charging and describing the way interest is charged, because it is (i) easy and (ii) legal compliance is guaranteed. Arguably, the approach also provides flexibility for issuers, enhancing the profile of the way in which interest is charged, and therefore increasing the scope for product differentiation on what is, after all, a key product feature.

Regulation Z details four principal methods of calculating interest. These are:

• Average Daily Balance
• Two-Cycle Average Daily Balance
• Adjusted Balance
• Previous Balance

A brief summary of these methods follows:

In 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. Assuming a balance remains roughly constant, the interest charge will remain the same regardless of the number of days in that cycle.

In Two-Cycle Average Daily Balance, it is the sum of the daily balances of the previous two cycles that is taken into account. Otherwise, the methodology remains the same.

With the Adjusted Balance method, the balance at the end of the billing cycle is multiplied by a factor in order to give the interest charge. Economically, this method is sub-optimal since it does not take into account the cost of lending throughout the month.

In the Previous Balance method, the reverse happens - the balance and the start of the previous billing cycle is multiplied by the interest factor in order to derive the charge. While this method is more profitable for the bank, it is uncompetitive for the customer, since (compared to Average Daily Balance) interest is charged on amounts that have already been paid off.

In addition to these methods, there is a Daily Accrual method, commonly used in the UK. In this method, the monthly rate is multiplied by 12, then 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 advantage of this method is that the interest charged exactly represents the cost of lending over the course of a month.

Difference Between ADB and Daily Accrual

In the United Kingdom, the two most common methods of calculating interest are Average Daily Balance (on cards issued by Barclaycard) and Daily Accrual (on cards issued through First Data).

In the Daily Accrual method, taking m to be the number of days in the billing cycle, the following formula is used to calculate the charge:

$\sum _{d=1}^{m}(bal_{d}*rate_{daily})$

In the ADB method, the following applies:

$\sum _{d=1}^{m}(bal_{d})*{\frac {rate_{monthly}}{m}}$

$\Longrightarrow \;\sum _{d=1}^{m}(bal_{d}*{\frac {rate_{monthly}}{m}})$

Ergo, interest could be considered to be accruing on a daily basis, at a daily rate equal to the monthly rate divided by the number of days in that billing cycle. In this way, the method is equivalent to a variable rate daily accrual, with a daily interest rate that changes month on month depending on the number of days in the relevant billing cycle.

From a consumer point of view, this then allows a more direct comparison between the merits of the two methods. For example, let us assume that a customer carries a debt of $1,000 for fifteen days before paying it off. In the daily accrual method, the interest charge will be:

$\ (1000*rate_{daily})*15$

$\rightarrow \;15000*rate_{daily}$

$\rightarrow \;15000*(rate_{monthly}*{\frac {12}{365}})$

$\rightarrow \;15000*{\frac {rate_{monthly}}{30.4}}$

In the ADB method, the charge will be:

$(15*1000)*{\frac {rate_{monthly}}{m}}$

$\rightarrow \;15000*{\frac {rate_{monthly}}{m}}$

It can therefore be concluded that if the billing cycle exceeds 30 days, then the interest charge will be lower under ADB. However, if the billing cycle is equal to 30 days or less, then Daily Accrual will be better value for the consumer.

External links

• Current US credit card interest rate averages
• US credit card interest rate trend graphs
• Monthly UK Debt Statistics Includes credit card rate averages