Oil is trading at $100 a barrel. The yield curve is flat at 5% (semi-annually compounded APR). The store cost of a barrel of oil for one year is $10, paid at the end of the year.

(a) What must be the forward price to purchase one barrel of oil in one year?

(b) Suppose the store cost of a barrel of oil suddenly drops to $5. The oil is still trading at $100 a barrel. What is the new forward price to purchase one barrel of oil in one year? Does it go up or down? Why?