Looking at the spot rates {r1, r2, ..., rt, ...}, Mr. Future decides to trade on existing discount bonds {B1, B2, ..., Bt, ...} in order to lock in the rate between year t-1 and year t, which is given by the forward rate ft.

a) Mr. Future thinks that trading on existing discount bonds is too much effort, instead, he wants to sign a forward contract with a bank which allows him to open a one-year saving account of $X in t-1 years. The saving rate quoted by the bank, denoted by st, is greater than ft (i.e., st > ft). is there an arbitrage opportunity? If yes, what is your strategy; and for every $1 saved with the bank, how much can you earn from this strategy?

b) If st < ft, is there still an arbitrage opportunity? If yes, show your strategy. If no, explain why.