Cash budget$-$Basic Grenoble Enterprises had sales of $$50,400$ in March and $$60,000$ in April. Forecast sales for May, June, and July are $$70,000,$$$80,000,$ and $$99,800,$ respectively. The firm has a cash balance of $$5,500$ on May $1$ and wishes to maintain a minimum cash balance of $$5,500.$ Given the following data, prepare and interpret a cash budget for the months of May, June, and July.

$(1)$ The firm makes $20\%$ of sales for cash, $65\%$ are collected in the next month, and the remaining $15\%$ are collected in the second month following sale.

$(2)$ The firm receives other income of $$1,900$ per month.

$(3)$ The firm's actual or expected purchases, all made for cash, are $$50,300,$$$69,900,$ and $$80,000$ for the months of May through July, respectively.

$(4)$ Rent is $$3,000$ per month.

$(5)$ Wages and salaries are $10\%$ of the previous month's sales.

$(6)$ Cash dividends of $$3,100$ will be paid in June.

$(7)$ Payment of principal and interest of $$4,300$ is due in June.

$(8)$ A cash purchase of equipment costing $$5,800$ is scheduled in July.

$(9)$ Taxes of $$5,700$ are due in June.

Complete the first month of the cash budget for Grenoble Enterprises below: $($Round to the nearest dollar. Please input all the values in the table before checking your answers.$)$

$\backslash$table$[[,,$arch,April,,May$],[$Sales$,$$$,50,400$$$,60,000,$$$,70,000],[$Cash sales,,$10,080,12,000,$$$,],[$Lag $1$ month,,,,$$,],[$Lag $2$ months,,,,$$,],[$Other income,,,,$$,],[$Total cash receipts,,,,$$,]]$