Rita Gipson owns 500 shares of Explore stock. The current price per share is $22.45. Rita is counting on having at least $10,000 from these shares six months from now to pay her college tuition, so she decided to purchase five European put options, each with 100 shares of Explore stock as underlier, ex- piration in six months, and a strike price of $2,000. The options each cost $30, and she withdraws the $150 to pay for them from her savings account that has a 4% annual effective interest rate. Six months from now, the price of a share of Explore stock is X, and Rita observes that buying the put option ended up increasing the total value of her holdings at time 6 months by $127.03. (a) Find X . (b) What is the largest amount by which buying the put options might have decreased the total value of her holdings at time 6 months?