A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is currently traded at $50 per share, and the 2-month, 3-month, 5-month, and 6-month risk-free rates are 3%, 3.025%, 3.05%, and 3.10% per annum with continuous compounding, respectively.

(a) What is the 6-month futures price on the stock? What is the initial value of the futures contract to a long position holder?

(b) If the price of the stock is $48 and the term structure of interest rates is unchanged in three months, what will be the futures price and the value of the short position in the futures contract?