An investor has invested $50,000 in a stock. Denote by [math]S_t[/math] the stock price at time [math]t[/math] expressed in years with [math]S_0[/math] the current stock price. Suppose [math]\ln(S_t/S_0) [/math] is normally distributed with mean [math]\mu = 0.05t [/math] and standard deviation [math]\sigma = 0.1\sqrt{t} [/math]. Determine the interval containing the 99^th percentile for the investor's $50,000 investment for a 30 day period. Assume 365 days in a year

• [46000, 50000]
• [52000, 55000]
• [58000, 60000]
• [75000, 77000]
• [77000, [math]\infty[/math]]