Hi, I need help with this question, please!! The gaming commission is introducin

Question

Hi, I need help with this question, please!!

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, $2,000 at the end of February, $3,000 at the end of March, and so on up to $12,000 at the end of December. At the beginning of the next year, the sequence repeats starting at $1,000 in January and ending at $12,000 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 1 million tickets, what is the minimum price they can charge for the tickets to break even, assuming the commission earns 6 percent/year/month on its investments and there is exactly one winning ticket.

Principle of Engineering Economic 6th Edition

Explanation / Answer

Annual interest = 6% / year

Thus, 6% = (1+ Monthly interest rate)^12 – 1

Monthly interest rate (R) = 1.06^(1/12) - 1 = .487%

Present value of one year payment = present value of $1000 payment + present value of arithmetic gradient $1000

Here, arithmetic gradient increases every month by $1000.

Present value of one year payment = 1000*(1-1/(1+R)^12)/R + 1000*((1+R)^12 - R*12 - 1)/(R^2*(1+R)^12)

Present value of one year payment = 1000*(1-1/1.00487^12)/.00487 + 1000*((1+.00487)^12 - .00487*12 - 1)/(.00487^2*(1+.00487)^12)

Present value of one year payment = $74912.834

Since, each year, $74912.834 is paid for perpetuity,

Thus, present value of perpetuity prize = 74912.834 / annual interest rate

Present value of perpetuity prize = 74912.834 / .06 = $1248547.23

No. of tickets = 1 million

Minimum price of the ticket= $1248547.23 / 1 million = $1248547.23/1000000

Minimum price of the ticket = $1.248 per ticket.

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