Gabrielle just won $2.5 million in the state lottery. She is given the option of receiving a total of $1.3 million now, or she can elect to be paid $100, 000 at the end of each of the next25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point of view which option should she take?

He should take annuity ahead of lump sum

Explanation:

Given that :

One time lump sum payment = 1,300,000

r = 5%

Period, t = 25 years

Cash flow, C= 100000v

A = C[1 - (1 + r)^-t] ÷ r

Hence,

100000×(1−(1.05)^−25)÷0.05

100000 * (1 - 0.2953027) ÷ 0.05

70469.722 / 0.05

= 1409394.4

The present value of the annuity is

$1,409,394.4

Annuity payment is greater Than lump sum

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