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Gabrielle just won ​$2.75 million in the state lottery. She is given the option of receiving...

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 ​$110,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her​ investments, from a strict economic point of view which option should she​ take? If Gabrielle takes the prize as an​ annuity, the present value of the 30​-year ordinary annuity is ​$ . ​(Round to the nearest​ dollar.)

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Answer #1

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

=$110,000[1-(1.05)^-25]/0.05

=$110,000*14.09394457

=$1,550,334(Approx).

Hence ​$110,000 at the end of each of the next 25 years is a better option.

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