Question

Congratulations, you just won the lottery!! The award was for $40,000,000. The lottery company has offered to either pay you the entire amount over 40 years at $1,000,000 per year, or they have offered you a chunk of money today (a lump sum) instead of receiving the $1,000,000 per year for 40 years. assuming a rate of 6%, what dollar amount does the lump sum need to be to be worth taking over the 1,000,000 per year for 40 years?

Answer 1

Present value annuity of $1,000,000 for 40 years is the amount which would be equivalent to either taking it now or in intervals for 40 years.

where, PVA = Present value annuity

P = payments made $1000000

r = rate of interest = 6%

n = number of time period = 40

PVA = P * [ 1 - ( 1 + r )^-n ] / r

PVA = 1000000 * [ 1 - ( 1 + 0.06 )^-40 ] / r

PVA = 1000000* [ 1 - 0.097222 ] / 0.06

PVA = 1000000 * 0.90277781 / 0.06

PVA = $15046296.87

Therefore. the lumpsum should be $15,046,296.87