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 $6 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 and the initial value of the forward contract?
b. Six months later, the price of the stock is $105 and the risk-free rate stays the same. What are the forward price and the value of the position in the forward contract?