Solve each of the following parts independently. $($Ignore income taxes.$)$ Please make sure your final answer$($s$)$ are accurate to the nearest whole number.

You can use the PV formulas in Excel or a financial calculator for these calculations.

a$)$ The XYZ Co$.$ Clinic can purchase a new computer system that will save $$10,000$ annually in billing costs. The computer system will last for $19$ years and have no salvage value. Up to how much should the XYZ Co$.$ Clinic be willing to pay for the new computer system if the clinic's required rate of return is $15\%?$

b$)$ The Las Vegas Times newspaper reported the following story: Bonnie Northrup of Las Vegas is the state's newest millionaire. By choosing the six winning numbers on last week's state lottery, Bonnie Northrup has won the week's grand prize totaling $$2\mathrm{.}38$ million. The State Lottery Commission has indicated that Bonnie Northrup will receive the prize in $28$ annual installments of $$85,000$ each. If Bonnie Northrup can invest money at a $10\%$ rate of return, what is the present value of the winnings?

c$)$ JenCo will need a new warehouse in $8$ years. The warehouse will cost $$500,000$ to build. What lumpsum amount should the company invest now to have the $$500,000$ available at the end of the $8-$year period? Assume that the company can invest money at $14\%.$