The Cypress Hills Furniture Corporation has a beginning cash balance of $$482$ on February $1$st$.$ The firm has projected sales of $$550$ in January, $$700$ in February, and $$800$ in March. The cost of goods sold is equal to $50\%$ of sales. Goods are purchased one month prior to the month of sale. The accounts payable period is $30$ days and the accounts receivable period is $15$ days. The firm has monthly cash expenses of $$200.$ What is the projected ending cash balance at the end of February? Assume that every month has $30$ days.