In exchange for a $$23,000$ payment today, a well$-$known company will allow you to choose one of the alternatives shown in the following table. Your opportunity cost is $9\%.$

Alternative Single amount

A $$28,500$ at end of $3$ years$$

B $$54,000$ at end of $9$ years$$

C $$160,000$ at end of $20$ years

a$.$ Find the value today of each alternative.

b$.$ Are all the alternatives acceptable? That is$,$ are they worth $$23,000$ today?

c$.$ Which alternative, if any, will you take?

Please show your work.