Relation between Inflation and Bank deposit interest rate?
The US doesn't have a long time series of deposit interest rates available for free. However, they do have one month CD data from 1966 to 2013. This is a short term loan to a bank, that pays a slightly higher interest rate than a savings account. It is widely available across banks and FDIC insured for smaller balances. The following figure compares those one month CD interest rates with the rate of inflation:



The correlation coefficient between these two series is 0.72. So they do move together (which is not surprising). However, you can see that there are long periods where there are large differences between the two series. Sometimes these differences are positive and other times they are negative.