Question

Rosie won the lottery today. She can receive 30 annual payments of $5,000,000 starting immediately. (So, the last installment will be received 29 years from today.) Alternatively, Rosie can opt to receive her entire winnings all at once today (a lump sum). If Rosie can invest at 6% per year, what minimum lump sum would make her choose to take her winnings at all once today?

Answer 1

This question requires application of PV of annuity due formula, according to which

1- (1 + i)- PV of an Annuity Due =R*- i *(1 + i)

$PV = 5,000,000 * [\frac{1-(1+0.06)^{-30}}{0.06}] * (1 + 0.06)$

PV = 5,000,000 * 13.76483 * 1.06

PV = $73,953,605.10