$($Present value of complex cash flows$)$ You have an opportunity to make an investment that will pay $$500$ at the end of the first year, $$400$ at the end of the second year, $$100$ a

third year, $$200$ at the end of the fourth year, and $$500$ at the end of the fifth year.

a$.$ Find the present value if the interest rate is $7$ percent. $($Hint: You can simply bring each cash flow back to the present and then add them up$.$ Another way to work this problem

$=$ NPV function in Excel or to use your CF key on a financial calculator$-$but you'll want to check your calculator's manual before you use this key. Keep in mind that with the $=$ NF

there is no initial outlay. That is$,$ all this function does is bring all the future cash flows back to the present. With a financial calculator, you should keep in mind that $C{F}_0$ is the initic

time $0,$ and, because there is no cash flow at time $0,C{F}_0=0.)$

b$.$ What would happen to the present value of this stream of cash flows if the interest rate were zero percent?

a$.$ What is the present value of the investment if the interest rate is $7$ percent?

$$,($Round to the nearest cent.$)$