Question

Gabrielle just won ​$2.75 million in the state lottery. She is given the option of receiving a total of ​$1,400,000 ​now, or she can elect to be paid ​$110,000 at the end of each of the next 25 years. If Gabrielle can earn 65% annually on her​ investments, from a strict economic point of view which option should she​ take? If Gabrielle takes the prize as an​ annuity, the present value of the 30​-year ordinary annuity is ​$ . ​(Round to the nearest​ dollar.)

Answer 1

PV of First Option = 1,400,000
PV of second Option = 110,000*(1-(1+65%)^-25/65%) = 169,230.15
I think rate is 6.5% and not 65% so i give you both answers
PV of second Option = 110,000*(1-(1+6.5%)^-25/6.5%) = 1,341,766.44

Hence getting 1.4 million now is better option

Annuity of prize money = 2,750,000/(1-(1+6.5%)^-30)/6.5% = 210,587.97 or 210,588

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