Ben decides to take a long position in 30 contracts of S&P 500 futures. Each contract is for the delivery of 250 units of the index at a price of 1500 per unit, exactly one month from now. The initial margin is 5% of the notional value, and the maintenance margin is 90% of the initial margin. Ben earns a continuously compounded risk-free interest rate of 4% on her margin balance. The position is marked-to-market on a daily basis.

(a) What is the notional value and the initial margin requirement of Bens long futures position?

(b) On the day of the first marking-to-market, the value of the index rises to 1501. On the day of the second marking-to-market, the value of the index is X and Ben is not required to add anything to the margin account. What is the minimum possible value of X?