A twenty five room budget motel expects its occupancy next year to be $80\%.$ The owner's present investment is $$200,800.$ They want an aftertax return on their investment of $10\%.$ Tax rate is $50$ percent.

Interest on a long$-$term mortgage is $10\%.$ Present balance outstanding is $$403,200.$

Depreciation is $10\%$ on building $($present book value is $$305,100)$ and $20\%$ on furniture and equipment $($present book value is $$75,000).$

Other fixed charges add up to $$70,900$ a year.

At an occupancy of $80\%,$ the motel's operating expenses $($wages$,$ supplies, laundry, and so on$)$ are calculated to be $$27,700$ a year.

The motel has other income $($from vending machines$)$ of $$2,600$ a year.

Rooms department direct expenses are $$10$ per room sold.

To cover all expenses and produce the net income required, what should the motel's average room rate be next year?