You can find an overview of how Savings Bonds work online at Treasury Direct. On this website there is information on Savings Bonds including Savings Bond Calculator, Savings Bonds Wizard, Value Files and FRB Locator and more.
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Savings bonds are an investment that will grant you interest based on how long you have the bond. The interest is comprised of either an annual or semiannual basis and will give you a larger sum over a longer period of time.
If you want to find a savings calculator online, I would check out http://www.bankrate.com/calculators/savings/simple-savings-calculator.aspx or if you find that unsatisfactory you can also use: http://apps.finra.org/calcs/1/savings Both calculators should work well!
Premium bonds are bonds that you buy that make you eligible to win a cash prize every month. Even if you do not win, your bonds will be 100% secure although you they may become less valuable over time due to inflation.
You can make your cash work harder by investing it in assets like stocks, bonds, or real estate, which have the potential to earn you more money over time than just keeping it in a savings account.
Economics 101 is a good place to start. Savings and loans corporations are there to make money work. People borrow and people save, that's the way of the world.