Please Show all work and formulas!

Problem 4

You have just won a lottery of $1 million and you can choose among the following three payout options. The effective annual interest rate (EAR) is 5%.

Option A: $200,000 right now and $100,000 every two years, starting 2 years from now and ending 16 years from now.

Option B: $100,000 a year at the end of the next 10 years, with the first payment one year from today.

Option C: Twenty annual payments of $40,000 and a 21^st payment of $200,000. The first payment is made right now. The 21^st payment is due 20 years from now.

Please calculate the present values of all three options. Which option should you choose?

Problem 5

Today is January 1, 2019, and your friend Arnold Armstrong signs a 4-year contract to play for a minor league football team. He will receive $300,000 for 2019, $500,000 for 2020, $700,000 for 2021, and $900,000 for 2022. All payments are made at the end of year. Assume 10% annual interest rate (EAR).

a. What is the present value of his contract?

b. If instead of annual payments he wants equal dollar amount month-end cheques over his contract period, starting January 31, 2019, how large is his monthly pay?