Clayton Kershaw, a dominating left-handed pitcher, is seeking to renew his contract with the L.A. Dodgers. The general manager (GM) of the Dodgers has offered Clayton two possible 5-year contracts: 

• Contract I: Clayton will receive a payment at the end of every month for five years (i.e. a total of 60 payments). The first payment will be for $675,000 (at the end of the first month), and all the subsequent payments will increase by 1% every month. In addition, Clayton will receive a signing bonus of $2 million payable now. 

• Contract II: Clayton will receive five equal payments of $10 million in the middle of each of the upcoming five years (i.e. the first payment will be received in 6 months, the second in 18 months, etc.). 

Suppose that Clayton can invest this money at an annual APR of 10%. 

(a) Find the present value of contract I. (

b) Find the present value of contract II. 

(c) Realizing that one of the contracts is not worth as much as the other, Clayton makes the following counter-offer to the Dodgers' GM. 

"I will accept the contract with the smaller present value if you add the following clause to it: At the end of every year, I shall receive one dollar per person in the attendance on the days that I pitch." 

Assuming that, as a starting pitcher, Clayton is expected to pitch 30 games a year, calculate the attendance (per game) that will make this modified contract worth as much as the other contract. You need to remember that these extra payments are due at the end of the year.