The current date is January 1st, 2021 and you have just won a lottery that offers you a choice in terms of payout. Your choices are as follows:

Choice 1: Payments of $100 per month from January 31st, 2021 to January 31st, 2031.

Payments of $200 per month from February 28th, 2031 to February 28th, 2041.

Choice 2: $1000 cash today.

Plus, payments of $15 per week forever, which grow at a real rate of 0.01% per week.

The initial $15 payment takes place on October 31 st, 2025.

Part A: If you have a real valuation rate of 3.0%, quoted as an annual percentage rate (APR), what is the present value of each offer?

Part B: What is the break-even number of periods? That is, how many payments (of $200) would Choice 1 need to offer in order to equate the present value of the two choices?

Part C: How would your answer to Part A change if you were given a real valuation rate of 5.0%, quoted as an annual percentage rate (APR)? Explain.