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Whether to use extra money to pay down debt or to invest is really dependent on your individual financial situation. You have to look at the types of debt you have, whether that debt is "good" debt or "bad" debt, and what your interest rates are.
"Good" debt is usually secured debt, and has a low interest rate. Things like a mortgage, home equity loan, or car loan are generally considered "good" debt. They generally reflect well on your credit report (unless you have a large amount of debt overall). Mortgage interest is usually tax-deductible, and so can save you a fair amount of money depending on the amount of interest you pay and what your tax bracket is. As long as you are making your payments on time, generally just paying the regular minimum payment is perfectly fine with secured debt.
"Bad" debt is unsecured. Things like credit cards and revolving lines of credit are generally considered "bad" debt, especially if you have large amounts of it. Having one credit card that you pay in full & on time each month doesn't affect your credit negatively (it generally helps your credit score). Carrying a balance on high-interest credit cards (and virtually all credit cards are high-interest, with rates of 10% or higher) is generally a bad idea.
Considering that most savings accounts are only returning in the range of 1% (or less) per year, and money market accounts are in the range of 5%, it usually makes more sense to pay down unsecured debt before investing or putting money into savings (beyond a few hundred dollars for emergencies).
Don't believe me?
Let's say that you have $5,000 in credit card debt, with a 10% interest rate, and you happen to get a $5,000 bonus at work. You consider paying off your credit card, but instead decide to put that money into a six month CD at your bank with a 5% APR. At the end of the six months, you have $5,125 (a gain of $125). You've made payments of $600 ($100 each month) on your credit card during the same time period. The amount of those payments going to interest is $242.81, and the amount going toward the principle is $357.19. So, you still owe $4642.81 on your credit card. If you paid the amount off now, you'd have $482.19 left over (minus the $600 you paid on the card over the past six months), leaving you worse-off by $117.81 than you were in the beginning. It will take you more than a full month of saved credit card payments to make up the difference. And that's only if you pay off your credit card after the six months! If
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