Do the following present value problems. You must set up all present value problems before calculation. Merely writing down the answer $($even if it is correct$)$ is an automatic zero. You must show your work. a$.$ Suppose we have a four year fixed$-$payment loan with $$1000$ payments made at the end of each year. Given a market interest rate of $8$ percent, how much was initially borrowed? b$.$ Suppose you were considering purchasing a $$6500$ machine today that would generate additional net profit of $$2500$ booked at the end of each year. Assuming you need an $8$ percent overall return to justify the investment, would the investment be worth doing if you had four years of payouts? Why or why not? Would your answer change if you had five years of $$2500$ payouts? Why or why not? You must use the concept of present value to demonstrate your answer, and show your work.