The possible stock prices for XYZ Corporation over the next two years are: Year 0 1 2 S_uu= 70 P_uu= S_u= 60 P_u= S_ud=50 P_ud= S= 50 P= S_d= 40 P_d= S_dd = 30 P_dd= The risk-free interest rate is 10% per year and the stock pays no dividends. Consider a European put with an exercise price of $50 and a time to expiration of 2 years.

Question:

Construct a synthetic bond with the stock and put in year 0 and compute the implied interest rate.