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When you do your savings rates comparison before you open a savings account, you will get a relative indication of the other types of rates your bank charges.
For instance, when saving account rates are high, then loan rates are probably high as well. The reason for this is that when the bank is making a large enough profit from the loans it gives they can afford to pay more in savings account rates because loans are the underlying investment for savings accounts.
If savings account rates are low it could indicate that loan rates are low. Generally, when the credit environment is slow and people are not taking out loans, the Federal Reserve will lower the federal interest rates (also called prime rate) in an effort to bolster consumer confidence and encourage consumers to take more loans. With more loans in the works it is possible that interest rates could go up on loans which would increase the interest rate in your savings account.
So remember, savings accounts are not in an ecosystem of their own. They are affected by and a result of the current credit and economic environment.