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.]

Chuck says

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.

Wai Yip Tung says

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

Harry Sit says

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.

Wai Yip Tung says

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.

KS says

TFB,

Don’t carry a balance, you say? According the the Federal Reserves 2007 Survey of Consumer Finances, 46% of the Americans surveyed have credit card balances. So, where do you get of saying, “enough said” regarding telling people to not carry a balance? People carry balances and that’s a fact of life, unfortunately for those balance carriers, but, fortunately, for banks, a system has been designed and concocted to exploit those balances. People need to carry balances for various reasons, good and bad, banks know that, so they hire mathematicians to create better ways to exploit those people and nickel and dime them to death. A very close friend of mine made his last credit card payment, on time, to one of these scam artist multi-billion dollar bank loan-sharks, and as soon as the check cleared (he called his bank to check everyday until it did), he then called to check his credit card balance which was now ZERO. But thanks to AVERAGE DAILY BALANCE, they tried to scam another $9.00 out of him on the next statement he received. So, basically they took a balance amount that NO LONGER EXISTED and averaged it with ZERO, and somehow came up with $9.00. Average daily balanced is flawed and it is a problem. Enough said.

Harry Sit says

KS – I’m so sorry you still don’t understand the basic principle of interest. If your friend paid after the statement close date (but before the due date), there are days between the statement close date and the date the payment is received during which he was still using money from the bank. If you use other people’s money, you pay interest. It has nothing to do with average daily balance.

Carrying a balance is a consenting adult’s choice. If it’s a fact of life, so is paying interest on days when money is borrowed. Here’s a simple form you can fill out for the calculation:

(1) Statement closed on ____________. Balance = ________.

(2) Payment received on ____________.

(3) # Days balance was outstanding = __________.

(4) Interest = __________ (Balance * APR / 365 * # of days)

Elaine says

I cannot seem to locate a formula that can explain Fidelity’s calculations. I thought I followed what they say but damn if I can get their numbers.

Take beginning Balance, Add amount applicable to the Daily Periodic Rate x the previous days daily balance. Add new purchases, Add new fees, Subtract payments and credits.

Also another question if my interest rate is 13%APR by adding a fraction of a percentage with each day does that not increase the actual APR???

I found several standard ADB calculators and the fee that determines is always lower than what I am paying.

THANK YOU!

Matt says

A fairer method would be to apply interest only to the dollars not paid off at the end of the month. I recently paid interest, something I rarely do, because I paid off my credit card before the statement date and another charge found itself on the card from another user in the meantime. I had a large charge amount on my account that I paid off within a few days of charging it, but because the charge increased my daily balance, I was charged for the entire amount of interest for the month. In reality, I used only a few days of that money and the interest I was charged was an inordinate amount considering my balance during the rest of the month. Needless to say, that bank card is no longer being used.

Had the bank charged me only for what I had remaining at the end of the month, which is ethical and should be the method they use, I would have paid a significantly smaller amount of interest. Instead they decided to try to teach an 820 a lesson and would not relent for a lousy $30 and change. Now the bank won’t even get transaction charges from me. Their loss. I used to charge upwards of $4k on that card with hundreds of transactions each month, but no longer. Another, more forgiving card that uses a method similar to my proposal is getting my business now. They calculate average daily balance, but subtract in-month payments from the overall calculation.