Motors Corporation manufactures motors for dirt bikes. The company requires a minimum $$30,000$ cash balance at each month$-$end. If necessary, the company borrows to meet this requirement at a cost of $3\%$ interest per month $($paid at the end of each month$).$ Any preliminary cash balance above $$30,000$ at month$-$end is used to repay loans. The cash balance on July $1$ is $$25,000,$ and the company has no outstanding loans. Budgeted cash receipts and budgeted cash payments $($other than for interest on the loan and loan activity$)$ follow.

July August September

Cash receipts $ $76,000$ $ $102,000$ $ $141,000$

Cash payments $104,00090,900118,400$