In our class example, I simplified the "annuity" prize option by assuming level, equal annualpayments. Actually, this annuity prize option us now on an annuitized prize payment schedule with 30 beginning of year payments that start at a lower amount with each successive payment being 5% higher than the previous annual payment. The sum of these 30 annuitized payments equal the announced estimated jackpot amount with a lower one-time lump-sum payment also being available as the Cash Option.

A recent Mega Millions estimated jackpot amount is $200 million which is the undiscounted sum of the 30 annuity option payments with a Cash Option of $138 million. The first payment under the Annuity Option which would occur immediately is $3,010,300 with 29 additional annual payments with each payment being 5% larger than the previous one. Using this information and assuming you demand a 3.5% annual return, would you prefer the Annuity Option or the Cash Option if you have the winning ticket?

I am confused on what annuity is and which equation to use for the annuity payments. I am also not sure how to split up the "payments" to increase 5% each time and I don't understand how the 3.5% annual return fits into this question? What is the difference between cash option and annuity?