Question

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $1,000 at the end of January, $1,900 at the end of February, $2,800 at the end of March, and so on up to $10,900 at the end of December. At the beginning of the next year, the sequence repeats starting at $1,000 in January and ending at $10,900 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 800,000 tickets, what is the minimum price they can charge for the tickets to break even, assuming the commission earns 12.00 %/year/month on its investments and there is exactly one winning ticket

Answer 1

$0.73

Step-by-step explanation:

Interest = 12% = 1% per month

The sequence of monthly payment for indefinite years

$1000, $1900, $28000......... $10900

This means that the monthly payment increases by $900

The equivalent monthly payment can be calculated as

= 1000 + 900 ( A/G , 1% , 12 )

= 1000 + 900 * 5.3814

= 1000 + 4843.26

= $5843.26

present worth of withdrawal = 5843.26 / 1% = $584326

The minimum price that the company will have to sell its ticket to breakeven

= 584326 / 800000

= $0.73