Question

Juan just won $2.5 million in the state lottery. He is given the option of receiving a total of $1.3 million now, or he can elect to be paid $100,000 at the end of each of the next 25 years. If Juan can earn 5% annually on his investments, from a strict economic point of view, which option should he take? Explain why.

Answer 1

Lottery amount lump sum given today =	1300000
Present value is	1300000
or
Annuity at end of year =	100000
No. of annuities =	25
Interest rate =	5%
Present value of annuity formula =	Annuity * (1- (1/(1+r)^n))/r
(100000*(1 - (1/(1+5%))^25)/5%
1409394.46
Present value of $100000 received for next 25 years is $1,409,394.46
So, He will choose lottery amount in installments of $100000 in next 25 years as present value is more in this case than lump sum amount of $1,300,000.

please thumbs up.