$1.$ A $$50,000$ cash bonus is paid now.

$2.$ A $$10,000$ annual cash bonus to be paid each year for the next five years at the end of each year, plus the first $$10,000$ paid now $($six times the payment of a $$10,000$ annual bonus in total. It is basically an annuity due case with n $=6).$

$3.$ A three$-$year $$22,000$ annual cash bonus with the first payment due three years from now. For example, today is$(01)/(01)()/(2021)($Year $1$ beginning$),$ and the first payment is$(01)/(01)()/(2024)($Year $4$ beginning, or$(12)/(31)()/(2023)),$ which is $3$ years after year $1.$

$1.$ Assume Sally can earn annually a $6\%$ return on her investments. What are the present values of the first, second, and third alternatives, respectively? Which alternative is the best for her?