Consider a forward contract on a non-dividend-paying stock with maturity 12 months. Assume the current stock price is $50 per share and the 1-year risk-free interest rate is 5% per annum (continuously compounded). (a) Compute todays arbitrage-free forward price of the stock per share. (b) Show that if the forward price is $55 per share then there exists an arbitrage opportunity. What is the arbitrage gain at maturity? (c) Show that if the forward price is $45 per share then there exists an arbitrage opportunity. What is the arbitrage gain at maturity?

(10 points) Consider a forward contract on a non-dividend-paying stock with maturity 12 months. Assume the current stock price is $50 per share and the 1-year risk-free interest rate is 5% per annum (continuously compounded). (a) Compute today's arbitrage-free forward price of the stock per share. (b) Show that if the forward price is $55 per share then there exists an arbitrage opportunity. What is the arbitrage gain at maturity? (c) Show that if the forward price is $45 per share then there exists an arbitrage opportunity. What is the arbitrage gain at maturity