Suppose that there is a forward contract on a non-dividend paying stock. The spot price of the stock is $80. The forward price is $83. The risk-free interest rate is constant at 5%.

What is the value of the forward contract?

Given the answer to a, is there an arbitrage opportunity available?

If there is an arbitrage opportunity, provide a strategy to exploit the arbitrage.

Suppose that the current index value for a stock market is 10000. The expected annual dividend yield for the stock index is 3% annually. What is the theoretical index value of a six-month futures contract on this stock index if the annual risk-free interest rate for borrowing and lending is 6%?

A one-year futures contract on a non-dividend-paying stock is entered into when the cash price for the stock is $30 and the risk-free interest rate is 10%.

What is the futures price today and what is the value of this futures contract?

Six months later, the stock price rises to $35 and the risk-free interest rate rises to 8%. What is the value of this futures contract at that time?