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 31, 2021 to January 31, 2031. 

 • Payments of $200 per month from February 28, 2031 to February 28, 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, 2025. 

 Calculate

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.