Economics - when quantitative easing was implemented and the Fed or Treasury bought back securities?

... from banks, since the interest rate was lower at that time did they pay the premium market value on those securities which were issued at higher

... from banks, since the interest rate was lower at that time did they pay the premium market value on those securities which were issued at higher interest rates? Wasn't this lowering of interest rates a way of creating equity for the banks and helped to reduce the amount of bailout loans to them?

or:... from banks, since the interest rate was lower at that time did they pay the premium market value on those securities which were issued at higher interest rates? Wasn't this lowering of interest rates a way of creating equity for the banks and helped to reduce the amount of bailout loans to them?

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