On March $1,1993,$ Elwood deposited $$4,200$ into a bank account. The account credited interest at a nominal interest rate of $4\%$ per year, compounded quarterly, when the balance was under $$5,000.$ The account credited interest at a nominal interest rate of $6\%$ per year, compounded semiannually, when the balance was at least $$5,000.$ Elwood withdrew $$1,000$ on March $1,1999.$ If there were no other deposits or withdrawals, determine Elwood$$s account balance on March $1,2003.($Assume that interest accrues continuously, not just at the end of a compounding period.$)$ The answer is $$5,420\mathrm{.}49$ but I$\text{'}$m not sure how to get there?