The Average Daily Balance Mystery

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.]