Stacey Trail has just won the Lotto.Her prize pays $40,000 at the end of each year for 5 years.In addition,she will receive a one-time payment of $240,000 at the end of 5 years.Using the following factors at 10%,what amount has Stacey really won in the Lotto?

Question

Quizplus · Accepted Answer

To determine the present value of the winnings, we need to use the present value factor for an annuity due for the annual payments of $40,000 for 5 years, and the present value factor for a single lump sum of $240,000 at the end of 5 years.

Using a 10% discount rate, the present value factor for an annuity due of 5 periods is 4.169. Therefore, the present value of the annual payments is:

PV = $40,000 x 4.169 = $166,760

Using the same discount rate, the present value factor for a single lump sum of 5 periods is 0.6209. Therefore, the present value of the one-time payment is:

PV = $240,000 x 0.6209 = $148,981

The total present value of Stacey's winnings is the sum of these two amounts:

PV = $166,760 + $148,981 = $315,741

Therefore, Stacey has really won $315,741 in the Lotto, which is closest to option B ($300,653).

Stacey Trail Has Just Won the Lotto