Question

A recent Mega Millions estimated jackpot amount is $300 million which is the undiscounted sum of the 26 annuity option payments with a Cash Option of $207 million. The first payment under the Annuity Option which would occur immediately is $4,515,432 with 29 additional annual payments with each payment being 5% larger than the previous one. Using this information and assuming you demand a 4% annual return, would you prefer the Annuity Option or the Cash Option if you have the winning ticket?

Answer 1

Answer:

Itis better to take the case in hand of 207,000,000 millions

Explanation:

We need to calcualte the present value of a geometric annuity-due

$\frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}$

g 0.05

r 0.04

C 4,515,432

n 26

n 26

$\frac{1-(1+0.05)^{26}\times (1+0.04)^{-26} }{0.04-0.05}$

 127,557,727.45

As is an annuity due, we multiply by (1+r)

127,557,727.45 x (1+0.04) = 132,660,036,548

The present value of the 207,000,000 option is better as the annuity present value is around 130,000,000