When someone wins a lottery jackpot they are often given the choice between receiving their winnings over some period of time or receiving less money but receiving it all at once. It makes the most economic sense to receive

a$.$ the reduced amount of money in one lump sum because it is always better to have money sooner rather than later.

b$.$ whichever option yields the lowest present value.

c$.$ the money over time because the amount received will be greater.

d$.$ whichever option yields the greatest present value.