please do C,d,e in 15 minutes will upvote

7. Consider A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock. (a) What is the difference between the forward price and the value of a forward contract? Provide formulas for the price & value of the contract at an arbitrary time t for a general, non-dividend-paying stock, assuming a constant risk-free interest rater and continuous compounding. (3 marks) (b) Explain why an investor may take a short position in a forward contract. (2 marks) (c) What is the forward price at time zero, and what is the value of the contract at time zero? (10 marks) (d) What is the forward price and the value of the contract 3 months later, if the price of the stock has become $48 and the interest is still 7% per annum? (10 marks) (e) Let T be the delivery period, r a risk-free rate and S the price of the underlying security that provides the holder with no income. Use arbitrage arguments to show how the forward price is calculated. (15 marks) (Total: 40 marks)