Question

You won the lottery and have a number of choices as to how to take the money. Which one of the following choices yields the greatest present​ value?

A.

​$12,000 a year at the end of each of the next 6 years using a​ 6% discount rate

B.

​$53,500 (lump​ sum) now using a​ 6% discount rate

C.

​$84,000 (lump​ sum) 7 years from now using a​ 6% discount rate

D.

​$92,000 (lump​ sum) 7 years from now using an​ 8% discount rate

Answer 1

a.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=12000[1-(1.06)^-6]/0.06

=12000*4.91732433

=$59007.89(Approx).

b.Present value=$53,500

c.Present value=84000*Present value of discounting factor(rate%,time period)

=84000/1.06^7

=84000*0.665057114

=$55864.80(Approx).

d.Present value=92000*Present value of discounting factor(rate%,time period)

=92000/1.08^7

=92000*0.583490395

=$53681.12(Approx).

Hence highest present value is of:

A.

​$12,000 a year at the end of each of the next 6 years using a​ 6% discount rate