A firm has projected credit sales of $$547,200$ for April and $$570,240$ for May. Credit purchases are $$211,680$ for April and $$252,720$ for May. Interest is $$16,410$ a month. Wages and other expenses are projected at $$57,240$ for April and $$69,420$ for May. The firm plans to purchase $$119,520$ of equipment in April, with additional purchases of $$131,040$ in May. The company predicts that $3\%$ of its credit sales will never be collected, $36\%$ of its sales will be collected in the month of sale, and the remaining $61\%$ will be collected in the following month. Credit purchases will be paid in the month following the purchase. In March, credit sales were $$302,400,$ and credit purchases were $$224,640.$ The April $1$ cash balance was $$386,200.$ What is the cash balance at the end of May?