You have an investment opportunity that promises to pay you $$20,000$ at a future date. You can earn $5\%$ compounded semiannually on similar investments.

Required:

How much would you be willing to invest assuming you will receive the amount at the end of $($a$)$ three years, $($b$)$ four years, or $($c$)$ five years?

If$,$ in addition to the $$20,000$ future value, you receive an additional $$1,000$ at the end of each semiannual period, how much would you be willing to invest assuming the investment spans $($a$)$ three years, $($b$)$ four years, or $($c$),$ five years?