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A little primer on inflation: Some people actually still hide money "under the mattress" in a place where it accumulates no interest. They are losing money every single day, in a very real way. Due to inflation, the money you have today will be worth slightly less tomorrow. In the US, annual inflation averages around the 3-4% range. So if it is 4% this year, that means that $1,000 today will be effectively worth $961 next year if it just sits under your mattress. It will still be $1,000 if you count it, but will only buy $961 of today's goods. Thus, in order to keep your money's value stable, you need to earn 4% on that money in the next year. Anything less and you'll be losing money, and anything more and you'll be gaining money.
Ok, so you need to keep up with inflation as best as you can. But if inflation is at 4%, and your bank's checking account only pays less than 1%, you're losing at least 3% of your money in the bank each year. How do you stop the bleeding?
One option that I like is the direct online savings accounts. Big real banks start online-only branches that give you very little service and have everything done electronically. Thus they avoid buildings, employees, and most all other costs. Then they give you a higher rate on your savings account than in their regular "bricks and mortar" banks. Right now you can get rates between 3% and 3.5% at some of these online savings accounts. They have links to your regular bank account and you transfer money back and forth as you wish. They typically have no fees, no minimums, and no restrictions.
If you want to look at a few for reference, try www.ingdirect.com, www.emigrantdirect.com, and www.hsbcdirect.com. And if you want to keep at least $1,000 in as a minimum, you can get a little higher rate at www.dollarsavingsdirect.com, which is also owned by Emigrant Bank. Make sure that where ever you put your money it is FDIC insured in case a bank implodes, and always read all the fine print when it comes to putting your money anywhere.