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Geometric Sequences and Exponential Functions

Identifying and using common ratios

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Credit: Chris Potter
Source: http://www.flickr.com/photos/86530412@N02/8266507462
License: CC BY-NC 3.0

Each year, credit card debt traps millions of Americans. Young people, especially those with their first job and first credit card, are at the greatest risk. How can credit card debt pile up so quickly? Is there any way to protect yourself from credit card debt?

Compounding Interest

Every credit card offer includes an annual percentage rate (APR). This is the rate of interest you’ll have to pay on your credit card debt. In theory, an APR of 20% means that for every $100 you carry on the card, you’ll have to pay back $120 at the end of the year. However, credit card companies don’t calculate interest due once a year; rather, most companies calculate the interest once a month and roll the interest due into the amount you owe them. The amount of money you owe increases like a geometric sequence. This means that if you owe $100 to the credit card company and don't pay it back, in one month you will owe a total of $101.67, in two months you’ll owe $103.36, in three months you’ll owe $105.08… and after twelve months you’ll owe $121.93. If the card compounds interest daily, you’ll have to pay even more. At first glance, this doesn’t seem like a high cost to pay—but the average American carries nearly $8,000 in credit card debt. When they miss a payment, their interest rates rise higher. They can easily become tangled in debts they can’t repay, and because of their bad credit, they’ll be unable to take out loans in order to buy cars or houses.

Credit: Wonderlane
Source: http://www.flickr.com/photos/wonderlane/5582186621/
License: CC BY-NC 3.0

How can you avoid getting trapped in a cycle of credit card debt? If you have a credit card, don’t treat it as short-term “money-lender.” Pay off your balance on time every month. Save up for big-ticket items. If you can’t afford to buy something with cash, don’t buy it with your card. Finally, make sure you’ve paid for housing, food, transportation, and utilities before you splurge on luxuries. Staying out of credit card debt is one of the best steps you can take to protect your future.

See for yourself: http://money.cnn.com/video/pf/2010/06/15/pf_hd_credit_debt_relief.moneymag/

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  1. [1]^ Credit: Chris Potter; Source: http://www.flickr.com/photos/86530412@N02/8266507462; License: CC BY-NC 3.0
  2. [2]^ Credit: Wonderlane; Source: http://www.flickr.com/photos/wonderlane/5582186621/; License: CC BY-NC 3.0

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