An investor has just taken a long position in a one-year forward contract on a dividend paying stock. The stock is expected to pay a dividend of $4 per share in five months and in eleven months. The stock price is currently selling for $100 and the risk-free rate of interest is 7% per year with continuous compounding for all maturities. a. What are the forward price (F₀=(S₀-I)e^rT) and the initial value of the forward contract? The forward price is (sample answer: $75.50) and the initial value is (sample answer: $75.50) b. Six months later, the price of the stock is $105 and the risk-free rate stays the same. What are the forward price (F₀=(S₀-I)e^rT) and the value of the position in the forward contract? Now the forward price is (sample answer: $75.50) and the value of the forward position is (sample answer: +$5.50; or -$5.50)

Please do not use CHATGPT I will downvote, Chatgpt always provides wrong answer.