Time Value of Money: For this question assume that the current date is January 1st, 2020. You recently won a lottery that offers you a choice between various payout schemes:

Payout X: Monthly payments of $150 from January 31st, 2020 to January 31st, 2030 In February 2030, monthly payments increase to $200. I.e. you will be paid $200 on February 28th, 2030. On February 28th, 2040 you receive a final payment of $750.

Payout Y: Monthly payments of $200 forever where the first payment is received at the end of January 2030 (i.e. on January 31st, 2030).

Payout Z: Receive $27,500 today. Assuming you have a real valuation (discount) rate of 5% APR, which would you choose? Make sure your answer includes the present value of each payout scheme.