The Average Daily Balance Mystery

April 28, 2010 by TFB

How to calculate interest on a loan should be very simple, but it seems to be a mystery to many people, including highly educated consumer advocates.

MSNBC.com columnist Bob Sullivan wrote a book Stop Getting Ripped Off: Why Consumers Get Screwed, and How You Can Always Get a Fair Deal. It was published around Christmas time last year. He spent five pages in the book trying to explain how credit card companies use the average daily balance method to calculate interest and how that method maximizes the revenue for the bank.

With the help of a spreadsheet created by blogger NCN at No Credit Needed, Sullivan showed that when a consumer doesn’t have a grace period because he’s carrying a balance, if he charged $3,000 on the 5th of the month (assuming the billing cycle runs from the 1st to the 30th), he would owe five times more interest than if he charged the same $3,000 on the 25th of the month. The author announced the surprise discovery:

"Putting off big-ticket purchases for twenty days can cut your interest charges by 80 percent!" [p. 85]

With that insight, our consumer advocate came up with a strategy: pay early, buy later.

Sullivan thinks there’s something unfair there — that the credit card companies use the average daily balance method to rip off consumers. After all, the title of the book is Stop Getting Ripped Off.

"Banks hire mathematicians to spend a lot of time trying to cook up formulas that are extremely advantageous to the banks." [p. 84]

"Spreading interest-rate charges over the maximum amount of days is a clever way to increase revenue." [p. 89]

I find it amazing how such a simple matter can get so convoluted. The whole exercise through the spreadsheet and all just showed he didn’t quite get how interest is supposed to work.

The basic principle for lending and borrowing is really simple:

If you use other people’s money, you pay interest.

In this basic form, it’s very easy to understand and I think everybody would agree that’s the way it should be. If you borrow money, you pay interest. If you borrow more money, you pay more interest. If you borrow the same amount of money for longer time, you pay more interest. If the amount and time are the same but the interest rate is higher, you pay more interest.

After you understand the basic principle, why is it any surprise that interest on a charge made on the 5th would be five times more than the same charged on the 25th? The charge on the 5th is borrowed for 25 days while the charge on the 25th is borrowed for 5 days. 25 days is five times of 5 days. Q.E.D.

I have a mathematical proof showing that calculating the interest by the amount borrowed times the number of days borrowed is exactly the same as applying the daily rate to the average daily balance for the month. In other words, the average daily balance method is consistent with the basic principle of lending and borrowing.

For the math inclined, let Ci be a charge and Di be the number of days borrowed. Let r be the daily interest rate and M be the number of days in a month. The interest for the month should be:

   SUM(Ci * Di * r)
= (SUM(Ci * Di) / M) * M * r
= Average Daily Balance * M * r

There is nothing unfair about the average daily balance method. Once one understands the basic principle of lending and borrowing, "pay early buy later" becomes so obvious — you don’t pay interest if you stop using other people’s money.

The average daily balance method isn’t the problem. Carrying a balance is. Don’t carry a balance. Enough said.

[Links to Amazon.com are affiliate links. Amazon pays me 4% - 6.5% if you make a purchase within 24 hours.]

Software picked, likely related posts:

Keywords:
Filed under: Banking and Credit Cards | Leave a comment

Comments

4 Comments on The Average Daily Balance Mystery

  1. Chuck on April 28, 2010 | permalink
     

    Sullivan must not realize that you can pay your credit card at any time. You don’t have to wait until your due date and keep watching the interest pile up. If you charge something on the 5th, you can make a payment for that purchase on the 10th and only pay 5 days of interest. I’ve yet to see a bank screw this up.

    (Even better, you can pay off your balance every month, and borrow money for free.)

    Average daily balance is good for the consumer because the interest only compounds monthly (from the date it is charged on the account). The bank could easily compound daily or continuously and charge you even more interest.

  2. Wai Yip Tung on April 28, 2010 | permalink
     

    Has the author come up with a “fairer” formula the bank should be using?

  3. TFB on April 28, 2010 | permalink
     

    Wai Yip Tung – No, but I have a feeling he’d like to see no interest for new purchases paid by the due date, regardless whether the cardholder paid the previous month’s bill in full or pay this month’s bill in full. Right now one has to meet both conditions to get an interest-free loan.

    In the following section the author suggested a “clean card” strategy: put all new charges one intends to pay in full on a different card. That’ll maximize the interest-free loan for the cardholder. If the cardholder always gets an interest-free loan for all new purchases, the “clean card” strategy wouldn’t be necessary.

  4. Wai Yip Tung on April 28, 2010 | permalink
     

    If he cannot come up with a different formula, it is another reason he has no ground to complain of being rip off.

    Getting interest free loan for the grace period is nice. But it is 21 days only and it only applies to new purchases. Having a “clean card” is smart. Other than that it is trivial amount of money that hardly worth strategizing. People should simply focus on paying off the credit card loan.

Tell me what you're thinking, but please don't spam. See comments moderation policy.