A question that vexes math students and teachers alike How does this apply to the rest of my life? turns out to have some surprising answers. Geometry in the living room? Statistics in your ledger? Yes, and yes.
Credit cards are ubiquitous in American life; there are probably 2 or 3 in your pocket right now. As of 2004, Americans were toting 1.3 billion total credit cards, and most of those cards users were feeling the pinch by the early part of this decade, average credit card debt for individuals had soared to over $11,000. During the same period, credit card companies lowered minimum payments so far that, for example, it may take a cardholder 32 years to pay off a simple $5000 balance at 15 interest. That s a scary figure.
In these times, it s absolutely critical to understand how compound interest works if you don t want to be stuck with out of control debt. However, many of us were absent that day in ninth grade math class, so here s a refresher.
Interest is, in effect, money that you pay or someone pays you for the privilege of borrowing money. When you put money in a savings account, the bank pays you a small amount of interest for the privilege of borrowing your money, and it works the same way when you borrow $50 from your credit card company to buy, say, that new season of Battlestar:Galactica on DVD. (Hey, I can relate.)
So let s say you put $100 in a savings account at a bank that offers an interest rate of 1 . Interest is calculated and added, generally, at certain time intervals monthly, six monthly, annually. Let s say your interest is calculated annually this means that at the end of the year your $100 in savings will contain your original $100, plus an amount of money equal to the principal ($100) multiplied by that interest rate of 1 . Percentages can also be expressed as decimals: 1 interest, for example, would be .001. 100 times .001 is 1, and that s the amount of interest you ve gained: $1. Add that to your original balance: you now have a whopping $101. If you d given your money to a bank that offered a slightly higher interest rate say, 3 you d be doing a bit better: 100 times .003 is $3, which added to that original $100 is $103.
That s simple interest. Compound interest is a little more, well, interesting it can make you a lot more money if you re the one receiving the interest, and it can hurt you a lot more if you re the one paying out. With compound interest, the money you earn in interest is added to the principal, so it s also gaining interest. Let s say you spend $100 on a credit card that charges monthly 20 compound interest. (What a wonderful world that would be!) If interest is figured monthly, then at the end of the first month you just owe $120.
At the end of the second month that $120 is the principal from which interest is calculated so now the amount of interest you owe isn t $20 as before, but 120 times .2, i.e. $124. At the end of the third month, interest is calculated again on that $124 you owe $24.8 in interest, but the credit card company rounds up, so $25 in interest is added, and next month you ll be paying interest on a whopping $149 debt.
This is why even a small credit card balance tends to spiral out of control. And since companies have used low monthly payments to lure in new customers who don t understand how compound interest works it becomes easier and easier for a small debt of $2000 5000 to become an onerous twenty or thirty year burden. (Many consumers don t realize that this is how the system is designed to work the longer you re paying off that little balance, the more interest the company makes.
Indeed, in the industry, the responsible card users who keep balances small and pay them off quickly are sometimes derogatorily referred to as deadbeats. )
But with a little understanding of compound interest and a little discipline, and, yes, a little luck (no sudden financial emergencies of the kind no one can plan for) you, too, can join the ranks of these deadbeats who refuse to be victims of the law of compound interest.
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