A one-year long forward contra

A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $50 and the risk-free rate of interest is 8% per annum with continuous compounding. What are the forward price and the initial value of the forward contract? Six months later, the price of the stock is $55 and the risk-free interest rate is still 8%. What are the forward price and the value of the forward contract?

Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, July, August, and November, dividends are paid at a rate of 4% per annum. In other months, dividends are paid at a rate of 2% per annum. Suppose that the value of the index on June 30 is 1,500. What is the futures price for a contract deliverable on December 31 of the same year?

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