Claudia used a credit card to help cover college expenses that has an an annual interest rate of $21\%$ compounded daily $($assume the credit card uses $365$ days in a year for calculations$).$ Suppose on September $1$st her balance was $$5213\mathrm{.}25$ and that she does not use the credit card to make any purchases in September. On September $30$th$,$ she makes a payment of $$200.$ What is her balance on October $1$st$?$