A stock is expected to pay a dividend of $3 in eight months. A one-year long forward contract on the stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

a. What are the forward price and the initial value of the forward contract?

b. Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%.

(i) What are the forward price, and change in forward price from six months ago.

(ii) Briefly describe in words what the value of the initial forward contract is.

(iii) Show the appropriate equation for calculating the value of the initial forward contract and then calculate the value of the initial forward contract if forward price is $49 now.