The TechEdge Corporation offers two forms of $4-$year service contracts on its closed$-$loop water purification system used in the manufacture of semiconductor packages for microwave and high$-$speed digital devices. The Professional Plan has an initial fee of $$57,000$ with annual fees starting at $$1,000$ in contract year $1$ and increasing by $$500$ each year. Alternatively, the Executive Plan costs $$62,000$ upfront with annual fees starting at $$1,000$ in contract year $1$ and decreasing by $$500$ each year. The initial charge is considered a setup cost for which there is no salvage value expected. Please find the present worth of the Professional plan as well as the Executive plan