A required reserve ratio of 6 percent means that banks have to keep 6% of their deposits in reserve and can loan out the rest. If we denote the required reserve ratio as R, in this problem R = 6 percent = 0.06.
We know that the formula for the money multiplier m = 1/R.
Since in this problem R = 6% or 0.06, the money multiplier m = 1/0.06 = 16.67.
If our bank decides to loan out the $550 of excess reserves, the maximum amount of money that the banking system can create after infinite rounds of money creation is given by the formula (m X Reserves) = 16.67 X $550 = $9,166.67.