A firm has invested $$40000$ in equipment with a $5-$year useful life. The machinery will have no salvage value. The annual benefits from the machinery are $$8000$ for the first year and increase by $$1500$ per year. Assume a combined $30\%$ state and federal income tax rate, and straight$-$line depreciation. Use interest rate $i=9\frac{\%}{?}$ year.

$($a$)(10$ points$)$ Calculate the present worth o this investment before taxes. b$)$ calculate the present worth after taxes