In order to determine what the Fed needs to do, we must first determine what the money multiplier is. The formula for finding the money multiplier is
Money multiplier = 1 / required reserve ratio.
In the scenario that you have given us, the required reserve ratio is .25. When we plug this into the money multiplier equation, we get
Money multiplier = 1 / .25 = 4.
This means that every new dollar that gets deposited in a bank can create a $4 increase in the overall money supply.
We also know that the Fed wants to create $100 billion in new money supply. We need to use the formula
Change in money supply = change in deposits x money multiplier.
Given that the money multiplier is 4, we can calculate that there needs to be a $25 billion increase in deposits.
So how does the Fed go about doing this? It cannot simply order people to deposit more money. Therefore, it needs to buy government securities. It needs to buy $25 billion in government securities. This money will be deposited in banks and the money multiplier will cause it to create a $100 billion increase in the money supply.