offers from various tech companies for the rights $to$ market your new invention. $To$ decide which offer $to$ accept, you must determine the $PVof$ each offer and choose the one that $is$ the highest.

Calculate the $PVof$ each offer listed below using $an8\%$ discount rate. Use the Appendices and then verify your answers using the time value functions $on$ your calculator.

$1.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$2,500,000$ payable $in10$ years.

$2.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$500,000$ now $+$ $$1,000,000in10$ years.

$3.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$250,000$ now $+$ $$250,000in5$ years $+$ $$500,000in10$ years.

$4.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$175,000$ per year for $10$ years $(ordinary$ annuity$).$

$5.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$200,000$ today $+$ $$125,000$ per year for $10$ years $(ordinary$ annuity$).$

$6.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}$ $$60,000$ per quarter for $10$ years $(ordinary$ annuity$).$

$7.{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{\text{\$}}150,000$ per year for $5$ years $+$ $$200,000$ per year for the next $5$ years.

The best option $of$ all the offers above $is{?}_{(}{)}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}{?}_{{?}_{?}}.$