Credit Card Mathematics

Credit Card Mathematics

As the last couple of mathematically related articles I've written have been kind of useless here is something eminently practical: periodic interest...i.e. the highway robbery of Credit Card companies.

First a brief history about credit cards. Prior to 1978, credit card/revolving loan providers were limited to about 12% interest rates. Most states capped interest rates under "Usury" laws. Usury is the term used by Christianity and Islam to describe the lending of money at an interest rate. It has now come to mean loaning money at rates that are excessive, or loan-sharkish. Only Islam remains steadfast in their commitment to ban the loaning of money at any interest rate. Admirably, at least to me, Muslim bankers prefer to make business loans in which they become a stake holder in the business. This has the advantage of ensuring that the bankers are business partners who are intimately tied into the success of the business and community, not just profiteers. That's pretty cool (and fits into my off-grid idealist perspective).

However in 1978 in Marquette vs. First Omaha National bank the Supreme Court ruled that it was permissible for a nationally chartered bank to "export" their interest rates. Basically, a loan originating in New York no longer had to adhere to a 12% loan. The banks could now charge the maximum interest allowed in the state of origination of the credit card. Delaware and South Dakota had the least amount of usury protection (for the consumer) and thus the major credit cards and lenders relocated their loans to these states. Thus credit card users can now be charged any amount of interest up to about 30%. Furthermore, almost any type of fee can be charged, and have almost no limits to their maximum amount.

Last, laws protecting the consumer from rate variance have significantly changed. For nearly any reason whatsoever, the credit card companies can change the terms of the loan, whenever they want. Imagine if mortgages worked that way...that would be frightening indeed! I wonder who thought that loosening controls on banks was a good idea anyway?

Anyhow, onto the math.

Interest is an easy calculation.

Let P = principal.

Let d = number of days that interest accrues before a payment is made.

Let r = daily periodic rate (an APR of 4% has a corresponding Daily Periodic rate of 4%/365)

Then your balance at the end of the month for a credit card is:

Balance = P*(1+r)^d

So for a credit card with 10,000 dollars on it, and an APR of 18% after one month we will accrue a balance of

10,000*(1+.18/365)^30 = 10149.01 dollars.

Or we end up paying 150 dollars in interest! After a year, if we pay 200$/month on the card we will still have a balance of...9335.371! Man that stinks!

At the rate of paying off 200$ a month it will take us more about 8 years to pay it off, and will have paid more than 7000$ in interest! Man that stinks!

In summary, if you have to use credit cards, then do so...but if not...then stay away! It's a bad deal. But the real question is, how can paying such high rates to banks be at all good for the economy? If we're all paying loads of interest to the banks we can't spend money on real goods. If we can't buy real goods, how can the economy provide jobs? If there aren't any jobs how can we pay back the interest?

For now it seems that wages are keeping up with loan repayments. What happens when that changes? How many people have to default on loans before the house of cards collapses? I suppose we'll see in the near future!

It seems that the banks may be pulling the rug out from under their feet in the long run... and definitely hurting the average working American in the short run.