Let S_t denote price of GOOG stock in year t. Today the spot price is S_0=871. S_1 has 40% chance of being 971 and 60% chance of being 771.

Let S_t denote price of GOOG stock in year t. Today the spot price is S_0=871.

S_1 has 40% chance of being 971 and 60% chance of being 771.

Find the range of risk-free rates r (risk-free interest rate is per annum with continuous compounding) such that you do NOT create an arbitrage opportunities when you initially take long OR short GOOG stock position at t=0 and then close out your position at t=1. (Note: this is only an arbitrage opportunity due to the model assumptions about S_1. In general, S_1 might reach $10^{100000} or $10^{ -100000} and so there is no bound on the range of r)