Question

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $700 at the end of January, $2,200 at the end of February, $3,700 at the end of March, and so on up to $17,200 at the end of December. At the beginning of the next year, the sequence repeats starting at $700 in January and ending at $17,200 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 900,000 tickets, the minimum price they can charge for the tickets to break even, assuming the commission earns 9.00 %/year/month on its investments and there is exactly one winning ticket.

Answer 1

The minimum price the gaming commission can charge for the tickets to break even is approximately $705.77.

Step-by-step explanation:

To calculate the minimum price the gaming commission can charge for the tickets to break even, we need to determine the present value of all the future cash flows. Present value is the current worth of a future stream of cash flows, taking into account the time value of money.

In this case, we have an infinite geometric sequence that starts with $700 and grows by $1,500 each month. The monthly interest rate is 0.09%/12 = 0.0075. We can use the formula for the sum of an infinite geometric series to calculate the present value.

PV = a / (1 - r)

Where PV is the present value, a is the first term, and r is the common ratio.

Plugging in the values, we get:

PV = $700 / (1 - 0.0075) = $700 / 0.9925 ≈ $705.77

Therefore, the minimum price the gaming commission can charge for the tickets to break even is approximately $705.77