Castor Incorporated is preparing its master budget. Budgeted sales and cash payments for merchandise purchases for the next three months follow.

Budgeted April May June

Sales $ $32,000$ $ $40,000$ $ $24,000$

Cash payments for merchandise purchases $20,20016,80017,200$

Sales are $50\%$ cash and $50\%$ on credit. Sales in March were $$24,000.$ All credit sales are collected in the month following the sale. The March $31$ balance sheet includes balances of $$12,000$ in cash and $$2,000$ in loans payable. A minimum cash balance of $$12,000$ is required. Loans are obtained at the end of any month when the preliminary cash balance is below $$12,000.$ Interest is $1\%$ per month based on the beginning$-$of$-$the$-$month loan balance and is paid at each month$-$end. If a preliminary cash balance above $$12,000$ at month$-$end exists, loans are repaid from the excess. Expenses are paid in the month incurred and include sales commissions $(10\%$ of sales$),$ shipping $(2\%$ of sales$),$ office salaries $($$$5,000$ per month$),$ and rent $($$$3,000$ per month$).$

$($a$)$ Prepare a schedule of cash receipts from sales for April, May, and June. $($b$)$ Prepare a cash budget for each of April, May, and June.