Question

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $800 at the end of January, $2,100 at the end of February, $3,400 at the end of March, and so on up to $15,100 at the end of December. At the beginning of the next year, the sequence repeats starting at $800 in January and ending at $15,100 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 1,150,000 tickets, what is the minimum price they can charge for the tickets to break even, assuming the commission earns 3.00 %/year/month on its investments and there is exactly one winning ticket

Answer 1

Step-by-step explanation:

3% per year

monthly interest =
`( 1.03 )^(1)/(12) -1`

= 1.00246 -1 = .246 %

Present value of cash flow = 780 + 2000.37 + 3160.93 + 4264.62+ 5313.48

+ 6309.52 + 7254.67 + 8150.8 + 8999.71 + 9803.16 + 10562.85 + 11280.40

= 77880.51

capitalised cost for this cash outflow for indefinite period

= 77880.51 / .03 = 2596017

no of tickets = 1150000

price per ticket for break even

= 2596017 / 1150000

= 2.257

price per ticket for break even = 2.257