I remember the night Visa found me. It was 1993 and I was living in England. I was working late at the Mathematical Institute in Oxford. The phone rang. I was used to getting calls from my friends at all hours of the night - for one thing because of the time difference with the United States, and for another thing because my friends are the kind of people who are awake at all hours of the night no matter what time zone they're in. But there was no friend on the other end of this line. Visa had found me.
I left college in 1991 with more debt than I could handle and a bad habit of letting myself forget about it for months at a time. During my senior year of college I had fought a pretty good bout against American Express. I won on points: they wrote off the debt, and I gave back the card. But with Visa I got on my bicycle. I thought if I rode it all the way to England, I'd be safe. I didn't count on my mother turning me in.
My grad school years were lean, but they were also fat, because in Berkeley we lived like paupers but ate like kings. If one of us got a fellowship check, all of us ate Roquefort. I liked to say back then that my friends and I would be the first graduate students in the history of graduate school to come down with gout.
None of this lent itself particularly well to paying bills. I remember when I was first beginning to date a particular young woman, and the two of us went back to my apartment for the first time. We walked in, and I flicked the light switch. Nothing. PG&E had shut me down. Gamely, she lit some candles, then said she'd be just a minute in the bathroom. Soon, word came through the closed door: no toilet paper. Gamely, she accepted the paper coffee filters I passed through to her. Gamely, she paid my electric bill the next day. Surprisingly after such a beginning, our relationship lasted another two and a half years.
But to return to the issue of credit. In my fourth year at Berkeley, Capital One, an unknown but clearly hungry new company, offered me my first credit card in years, with a thousand-dollar limit. I took them up on the offer. On the very same day the card arrived, I maxed it out with a plane ticket to Amsterdam. Somebody over at Capital One lost their job that day, I'm pretty sure. But it was legitimate! I was scheduled to give a paper at a conference on quantum mechanics. But I didn't have funding for the airfare, so the card arrived just in time. My relationship with Capital One has lasted to this day, and it's had all the ups and downs of any relationship, though in this case mostly to do with APRs.
People ask me mathematical questions all the time. A friend once sent me the following cryptic email:
pool of possible questions: 5
possible amount on test to choose from: 2 or 3.
number of questions to answer: 1.
If I just choose two questions to study, what are the odds of having one of those show up on the test as a posed question to answer?
More recently, a friend asked how best to pay off a high-interest credit card. She'd been paying $600 per month on a $10,000 balance at 21.9% interest, and she was now considering cashing in a 403(b) account to eliminate the debt. After finding out some more about the person's situation, I advised taking out a home equity line of credit to pay off the debt. Assuming she stops using the card completely, then in three years, she can have the home equity loan paid off, and by that time she can also have $10,000 cash reserves in the bank - all for the same $600 per month she's paying now on the credit card. (The caveat of course is that you really do have to stop using the credit card, otherwise in three years you'll just find yourself maxed out again.)
In my own life, I have often wondered, if I owe X amount on a credit card at Y% interest, and I pay Z per month, then how long will it take me to pay off the card, assuming I don't charge anything else on it? The mathematics required to answer this is not trivial. There are online calculators that will do the computation for you - see this one for example. But the downside of using a calculator is that you don't get any insight into the problem you're facing. So I sat down one day several years ago and derived the answer once and for all. Here it is:
In this formula, b_0 is the initial balance, p is what you have decided to pay every month, and i is the daily interest rate, that is, your APR divided by 365. Note that the payoff time N turns out to be a function not of b_0 and p separately, but rather a function of the ratio p/b_0. Physicists will have seen this coming, thanks to their penchant for dimensional analysis. (The answer to the problem - a number of months - has no dollar signs on it; so the dollar signs on p and b_0 have to be got rid of. The only way to do that is to work with the ratio p/b_0.)
The derivation is here.
Getting into the details of this problem gives you a gut-level feel for an important financial fact: payments to the credit card company are mathematically the same as investments that grow with a guaranteed rate of return. Millionaires pay ludicrous fees to hedge funds in exchange for a guaranteed rate of return. Schmucks like us can do the same thing just by overpaying our credit card bill.
For convenience, I have put together the following table, suitable for printing out and stashing away in the utility drawer (click to enlarge):
For example, suppose your starting balance is $10,000, your interest rate is 12.9%, and you figure you can afford to pay $400 per month. Your monthly payment equals 4% of the starting balance. So look down the 4% column until you get to the row for an APR of 13%. You see that it will take you 29 months to pay off the card, or about two and a half years. (After a few months of making payments, call the company every so often to request a lower APR.)
Another example. Your starting balance is $10,000, your interest rate is 12.9%, and you really want to have this card paid off in a year, because you're planning to refinance your house in 18 months, and you want your credit score to be as high as possible. [Can somebody tell me when I suddenly became this middle-aged??] Looking at the table in the 13% row, you see that in order to have a 12-month payoff time, you're going to have to pay 9% of the starting balance, or $900, every month.
I liked Jean Chatzky's advice on her financial webpage. But the trouble with Chatzky's program is that it has nine steps. Who can remember nine steps? Who can carry them out? The people who can follow nine steps are not the people with maxed-out credit cards. So, as a recovered credit-card delinquent, I thought I would share my own program, which is so simple it has only one step:
Tithe 10 percent.
Tithing 10 percent means that any time any money whatsoever comes into your household - be it a paycheck, tax refund, honorarium, royalty, or even a good night's poker winnings - sit down that very night and send a check to your credit card company for 10 percent of whatever amount you brought in that day. Don't even wait for your account statement; just keep those checks moving out the door.
(If you have more than one credit card bill, divide your 10% tithe among the various cards in a ratio that makes the most sense to you.)
If your annual net income is, say, $30,000 per year, then tithing will divert $3,000 a year to your credit card, and what's more that'll be on a continual basis, hammering away at the debt before interest can pile up. They say interest never sleeps; well, don't let your payments sleep either. Think of your steady stream of checks as a flurry of jabs that will keep the credit card companies constantly on their heels.
If your tithe isn't bringing the balances down, then you can increase the percentage, make an extra payment when the account statement comes in the mail, and, most important of all, STOP USING THE CARD.
The system works, because in all honesty you can probably spare 10% of whatever you make, especially if you part with it immediately. After all, with the money gone, you can't very well blow it on Roquefort, can you?