Question

You just won the Florida lottery. To receive your winnings, you must select one of the two following choices: You can receive $1,000,000 a year at the end of each of the next 30 years; OR You can receive a one time payment of $15,000,000 today. Assume that the current interest rate is 5 %. Which option is most valuable?

Answer 1

Case 1:

Periodic payments = P = $ 1,000,000 per year

No. of years = n = no. of periodic payments = 30

Interest rate = r = 5 % p.a. = 0.05 per annum per $

This scenario is nothing but annuity

So,

Present value of annuity = PV =  P x ((1 - (1 / (1 + r) ^ n)) / r) = 1,000,000 * (( 1- ( 1+0.05)^-30) )/ 0.05

= $ 153,724,510.2

Therefore, Present value of the Annuity = $ 15,372,451.02

Case 2:

Present value if accepted the payment = $ 15,000,000

Since, Present value of case 1 ( i.e., present value of annuity) is greater than Present value of case 2

i.e, 15,372,451.02 > 15,000,000

Therefore, Accept the case 1

Answer: Accept $1,000,000 a year at the end of each of the next 30 years;