A government data processing center has been plagued in recent years by complaints from employees of back pain. Consultants have estimated that upgrading office furniture at a net cost of $$40,000$ would reduce the incidence and severity of back injuries, allowing the center to avoid medical care that currently costs $$10,000$ each year. The furniture would have a useful life of five years, after which it would have zero salvage value. Assume the avoided costs occur at the end of each year. In its investment decisions, the center uses a nominal discount rate of $10$ percent and an assumed general inflation rate of $4$ percent.

a$.$ Using summation notation, write an expression for the NPV$,$ expressed in real dollars

b$.$ Using summation notation, write an expression for the NPV$,$ expressed in nominal dollars

c$.$ Using summation notation, write an expression for the NPV$,$ expressed in real dollars, assuming the cost of medical care will rise $3$ percent faster than other prices.

d$.$ Using summation notation, write an expression for the NPV$,$ expressed in nominal dollars, assuming the cost of medical care will rise $3$ percent faster than other prices.