In 2015, Major League Baseball player Chris Davis signed with the Baltimore Orioles for $161 million to play with the Orioles for 7 years. He and the Orioles agreed for him to be payed beyond the 7 years he was under contract. The payment plan for the contract was as follows:

$17 million each year for years 1 through 7.

$3.5 million each year for years 8 through 17.

$1.4 million each year for years 18 through 22.

You should assume that the Orioles pay Davis annually at the end of each year and that he receives the first $17 million at the end of the first year. Davis receives money for 22 years. If he signs another contract after 7 years, he would still receive the same amount of money as described above.

a) If the interest rate is 5% compounded annually, how much would the Orioles need to deposit in year 0 in order to fully fund this contract?

b) Davis had previously rejected a $154 million contract for 7 years. Assume that the $154 million contract would have been paid in 7 equal installments (i.e., $22 million per year) in which the first payment is made at the end of the first year. If Daviss interest rate is 5% compounded annually, which contract would you prefer from Daviss point of view? He can sign another contract after year 7 regardless of whether he signs the $161 or $154 million contract. (This is an open-ended question, but you should use the formulas and ideas from Chapter 3 to answer this question.)