The gaming commission is introducing a new lottery game called Infinite Progress

Question

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $1,200 at the end of January, $2,000 at the end of February, $2,800 at the end of March, and so on up to $10,000 at the end of December. At the beginning of the next year, the sequence repeats starting at $1,200 in January and ending at $10,000 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 1,200,000 tickets, the minimum price they can charge for the tickets to break even, assuming the commission earns 6.00 %/year/month on its investments and there is exactly one winning ticket.

Explanation / Answer

Present Value = (1200/6%)/(1+6%)^(1/12) + (2000/6%)/(1+6%)^(2/12) + (2800/6%)/(1+6%)^(3/12) + (3600/6%)/(1+6%)^(4/12) + (4400/6%)/(1+6%)^(5/12) + (5200/6%)/(1+6%)^(6/12) + (6000/6%)/(1+6%)^(7/12) + (6800/6%)/(1+6%)^(8/12)  + (7600/6%)/(1+6%)^(9/12) + (8400/6%)/(1+6%)^(10/12) + (9200/6%)/(1+6%)^(11/12) + (10000/6%)/(1+6%)^(12/12)

Present Value = $ 1,076,383.32

Minimum price they can charge for the tickets to break even = Present Value of Winning Amount/No of Ticket

Minimum price they can charge for the tickets to break even = 1,076,383.32/1200000

Minimum price they can charge for the tickets to break even = 0.90

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